## Biography

I received my Bachelor and Master degrees from Electrical Engineering Department, National Taiwan University, Taiwan in 1999 and 2001. I received my PhD degree in electrical engineering from the University of Southern California, Los Angeles, in 2008. In November 2008, I was employed as a research scientist with the ERATO-SORST Quantum Computation and Information Project, funded by the Japan Science and Technology Agency (JST). In September 2010, I became a postdoctoral research fellow in the Statistical Laboratory of the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge, UK.

I joined the University of Technology Sydney (UTS) as a Chancellor’s Postdoctoral Fellow in March 2012, and was immediately awarded a four-year, fixed term lectureship. In October 2013, I was promoted to the continuing position of Senior Lecturer. In July 2014, I was awarded a Future Fellowship from the Australian Research Council, and promoted to the position of Associate Professor. I am currently the leader of the program "Quantum information theory and security", one of the five key research programs within the Centre of Quantum Software and Information (UTS:QSI).

#### Can supervise: YES

#### Research Interests

My research interests include general topics in quantum information and computation.

#### Publications

Cheng, HC & Hsieh, MH 2019, 'Matrix Poincaré, Φ -Sobolev inequalities, and quantum ensembles', *Journal of Mathematical Physics*, vol. 60, no. 3.View/Download from: Publisher's site

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© 2019 Author(s). Sobolev-type inequalities have been extensively studied in the frameworks of real-valued functions and non-commutative Lp spaces, and have proven useful in bounding the time evolution of classical/quantum Markov processes, among many other applications. In this paper, we consider yet another fundamental setting - matrix-valued functions - and prove new Sobolev-type inequalities for them. Our technical contributions are two-fold: (i) we establish a series of matrix Poincaré inequalities for separably convex functions and general functions with Gaussian unitary ensembles inputs; and (ii) we derive Φ-Sobolev inequalities for matrix-valued functions defined on Boolean hypercubes and for those with Gaussian distributions. Our results recover the corresponding classical inequalities (i.e., real-valued functions) when the matrix has one dimension. Finally, as an application of our technical outcomes, we derive the upper bounds for a fundamental entropic quantity - the Holevo quantity - in quantum information science since classical-quantum channels are a special instance of matrix-valued functions. This is obtained through the equivalence between the constants in the strong data processing inequality and the Φ-Sobolev inequality.

Cheng, HC, Gao, L & Hsieh, MH 2019, 'Properties of Scaled Noncommutative Rényi and Augustin Information', *IEEE International Symposium on Information Theory - Proceedings*, vol. 2019-July, pp. 2219-2223.View/Download from: UTS OPUS or Publisher's site

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© 2019 IEEE. The scaled Rényi information plays a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error exponent analysis. In quantum information theory, there are three generalizations of the classical Rényi divergence - the Petz's, sandwiched, and log-Euclidean versions, that possess meaningful operational interpretation. The goal of this paper is thus to analyze fundamental properties of scaled Rényi information from a noncommutative measure-theoretic perspective. Firstly, we prove the uniform equicontinuity for all three quantum versions of Rényi information, hence it yields the joint continuity of these quantities in the orders and priors. Secondly, we establish the concavity in the region of s ∈ (-1, 0) for both Petz's and the sandwiched versions. This completes the open questions raised by Holevo, Mosonyi and Ogawa. For the applications, we show that the strong converse exponent in classical-quantum channel coding satisfies a minimax identity. The established concavity is further employed to prove an entropic duality between classical data compression with quantum side information and classical-quantum channel coding, and a Fenchel duality in joint source-channel coding with quantum side information.

Cheng, HC, Hanson, EP, Datta, N & Hsieh, MH 2019, 'Duality between source coding with quantum side information and c-q channel coding', *IEEE International Symposium on Information Theory - Proceedings*, vol. 2019-July, pp. 1142-1146.View/Download from: Publisher's site

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© 2019 IEEE. In this paper, we establish an interesting duality between two different quantum information-processing tasks, namely, classical source coding with quantum side information, and channel coding over classical-quantum channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an optimal coding strategy for one task can be used to construct an optimal coding strategy for the other task. Along the way, we derive a bound on the error exponent for classical-quantum channel coding with constant composition codes which might be of independent interest.

Salek, F, Hsieh, MH & Fonollosa, JR 2019, 'Publicness, Privacy and Confidentiality in the Single-Serving Quantum Broadcast Channel', *IEEE International Symposium on Information Theory - Proceedings*, vol. 2019-July, pp. 1712-1716.View/Download from: Publisher's site

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© 2019 IEEE. The 2-receiver broadcast channel with primary and third-party receivers is studied. The messages are classified into public, private and confidential. The messages in the public class are messages intended for both receivers. The private messages are intended for the primary receiver with no secrecy requirements imposed upon them. And the confidential messages are aimed exclusively to the primary receiver such that they must not be accessible to the other receiver. The encoder performs the necessary encryption by virtue of local randomness whose rate is assumed to be limited. We find an achievability region on the trade-off between the rates of the three messages and the source of randomness in the one-shot regime of a quantum broadcast channel.

Zhu, EY, Zhuang, Q, Hsieh, MH & Shor, PW 2019, 'Superadditivity in trade-off capacities of quantum channels', *IEEE Transactions on Information Theory*, vol. 2018.View/Download from: UTS OPUS or Publisher's site

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IEEE In this article, we investigate the additivity phenomenon in the quantum dynamic capacity region of a quantum channel for trading the resources of classical communication, quantum communication, and entanglement. Understanding such an additivity property is important if we want to optimally use a quantum channel for general communication purposes. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity region, and it is largely unknown if this could lead to a strictly superadditive double or triple resource capacity region, respectively. For example, if a channel has additive classical and quantum capacities, can the classical-quantum capacity region be strictly superadditive? In this work, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple resource capacity region for a given channel.

Anshu, A, Hsieh, M-H & Jain, R 2018, 'Quantifying Resources in General Resource Theory with Catalysts.', *Physical review letters*, vol. 121, no. 19.View/Download from: UTS OPUS or Publisher's site

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A question that is commonly asked in all areas of physics is how a certain property of a physical system can be used to achieve useful tasks and how to quantify the amount of such a property in a meaningful way. We answer this question by showing that, in a general resource-theoretic framework that allows the use of free states as catalysts, the amount of "resources" contained in a given state, in the asymptotic scenario, is equal to the regularized relative entropy of a resource of that state. While we need to place a few assumptions on our resource-theoretical framework, it is still sufficiently general, and its special cases include quantum resource theories of entanglement, coherence, asymmetry, athermality, nonuniformity, and purity. As a by-product, our result also implies that the amount of noise one has to inject locally to erase all the entanglement contained in an entangled state is equal to the regularized relative entropy of entanglement.

Cheng, HC & Hsieh, MH 2018, 'Moderate deviation analysis for classical-quantum channels and quantum hypothesis testing', *IEEE Transactions on Information Theory*, vol. 64, no. 2, pp. 1385-1403.View/Download from: UTS OPUS or Publisher's site

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© 1963-2012 IEEE. In this paper, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate lower than 1 {n} , a research topic known as moderate deviation analysis. We show that the optimal error probability vanishes under this rate convergence. Our main technical contributions are a tight quantum sphere-packing bound, obtained via Chaganty and Sethuraman's concentration inequality in strong large deviation theory, and asymptotic expansions of error-exponent functions. Moderate deviation analysis for quantum hypothesis testing is also established. The converse directly follows from our channel coding result, while the achievability relies on a martingale inequality.

Chitambar, E, Fortescue, B & Hsieh, MH 2018, 'The Conditional Common Information in Classical and Quantum Secret Key Distillation', *IEEE Transactions on Information Theory*, vol. 64, no. 11, pp. 7381-7394.View/Download from: UTS OPUS or Publisher's site

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© 2018 IEEE. In this paper, we consider two extensions of the Gács-Körner common information to three variables, the conditional common information (cCI) and the coarse-grained conditional common information (ccCI). Both quantities are shown to be useful technical tools in the study of classical and quantum resource transformations. In particular, the ccCI is shown to have an operational interpretation as the optimal rate of secret key extraction from an eavesdropped classical source pXYZ when Alice (X) and Bob (Y) are unable to communicate but share common randomness with the eavesdropper Eve (Z). Moving to the quantum setting, we consider two different ways of generating a tripartite quantum state from classical correlations pXYZ : 1) coherent encodings ∑xyz√pxyz|xyz〉 and 2) incoherent encodings ∑xyzpxyz|xyz〉〈xyz|. We study how well can Alice and Bob extract secret key from these quantum sources using quantum operations compared with the extraction of key from the underlying classical sources pXYZ using classical operations. While the power of quantum mechanics increases Alice and Bob's ability to generate shared randomness, it also equips Eve with a greater arsenal of eavesdropping attacks. Therefore, it is not obvious who gains the greatest advantage for distilling secret key when replacing a classical source with a quantum one. We first demonstrate that the classical key rate of pXYZ is equivalent to the quantum key rate for an incoherent quantum encoding of the distribution. For coherent encodings, we next show that the classical and quantum rates are generally incomparable, and in fact, their difference can be arbitrarily large in either direction. Finally, we introduce a "zoo" of entangled tripartite states all characterized by the conditional common information of their encoded probability distributions. Remarkably, for these states almost all entanglement measures, such as Alice and Bob's entanglement cost, squashed entanglement, and relative entropy of...

Vijayan, MK, Chitambar, E & Hsieh, M-H 2018, 'One-shot assisted concentration of coherence', *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, vol. 51, no. 42.View/Download from: UTS OPUS or Publisher's site

Cheng, HC, Hsieh, MH & Tomamichel, M 2017, 'Exponential decay of matrix Φ-entropies on Markov semigroups with applications to dynamical evolutions of quantum ensembles', *Journal of Mathematical Physics*, vol. 58, no. 9.View/Download from: UTS OPUS or Publisher's site

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In this work, we extend the theory of quantum Markov processes on a single quantum state to a broader theory that covers Markovian evolution of an ensemble of quantum states, which generalizes Lindblad's formulation of quantum dynamical semigroups. Our results establish the equivalence between an exponential decrease of the matrix Φ-entropies and the Φ-Sobolev inequalities, which allows us to characterize the dynamical evolution of a quantum ensemble to its equilibrium. In particular, we study the convergence rates of two special semigroups, namely, the depolarizing channel and the phase-damping channel. In the former, since there exists a unique equilibrium state, we show that the matrix Φ-entropy of the resulting quantum ensemble decays exponentially as time goes on. Consequently, we obtain a stronger notion of monotonicity of the Holevo quantity-the Holevo quantity of the quantum ensemble decays exponentially in time and the convergence rate is determined by the modified log-Sobolev inequalities. However, in the latter, the matrix Φ-entropy of the quantum ensemble that undergoes the phase-damping Markovian evolution generally will not decay exponentially. There is no classical analogy for these different equilibrium situations. Finally, we also study a statistical mixing of Markov semigroups on matrix-valued functions. We can explicitly calculate the convergence rate of a Markovian jump process defined on Boolean hypercubes and provide upper bounds to the mixing time. Published by AIP Publishing.

Chitambar, E & Hsieh, MH 2017, 'Round complexity in the local transformations of quantum and classical states', *Nature Communications*, vol. 8, no. 1.View/Download from: UTS OPUS or Publisher's site

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© 2017 The Author(s). In distributed quantum and classical information processing, spatially separated parties operate locally on their respective subsystems, but coordinate their actions through multiple exchanges of public communication. With interaction, the parties can perform more tasks. But how the exact number and order of exchanges enhances their operational capabilities is not well understood. Here we consider the minimum number of communication rounds needed to perform the locality-constrained tasks of entanglement transformation and its classical analog of secrecy manipulation. We provide an explicit construction of both quantum and classical state transformations which, for any given r, can be achieved using r rounds of classical communication exchanges, but no fewer. To show this, we build on the common structure underlying both resource theories of quantum entanglement and classical secret key. Our results reveal that highly complex communication protocols are indeed necessary to fully harness the information-theoretic resources contained in general quantum and classical states.

Cheng, H-C & Hsieh, M-H 2016, 'Characterizations of matrix and operator-valued Phi-entropies, and operator Efron-Stein inequalities', *PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, vol. 472, no. 2187.View/Download from: UTS OPUS or Publisher's site

Cheng, H-C & Hsieh, M-H 2016, 'Concavity of the Auxiliary Function for Classical-Quantum Channels', *IEEE TRANSACTIONS ON INFORMATION THEORY*, vol. 62, no. 10, pp. 5960-5965.View/Download from: UTS OPUS or Publisher's site

Cheng, H-C, Hsieh, M-H & Yeh, P-C 2016, 'THE LEARNABILITY OF UNKNOWN QUANTUM MEASUREMENTS', *QUANTUM INFORMATION & COMPUTATION*, vol. 16, no. 7-8, pp. 615-656.View/Download from: UTS OPUS

Chitambar, E & Hsieh, M-H 2016, 'Relating the Resource Theories of Entanglement and Quantum Coherence', *PHYSICAL REVIEW LETTERS*, vol. 117, no. 2.View/Download from: UTS OPUS or Publisher's site

Chitambar, E, Hsieh, M-H & Winter, A 2016, 'The Private and Public Correlation Cost of Three Random Variables With Collaboration', *IEEE TRANSACTIONS ON INFORMATION THEORY*, vol. 62, no. 4, pp. 2034-2043.View/Download from: UTS OPUS or Publisher's site

Datta, N, Hsieh, M-H & Oppenheim, J 2016, 'An upper bound on the second order asymptotic expansion for the quantum communication cost of state redistribution', *JOURNAL OF MATHEMATICAL PHYSICS*, vol. 57, no. 5.View/Download from: UTS OPUS or Publisher's site

Hsieh, M-H & Watanabe, S 2016, 'Channel Simulation and Coded Source Compression', *IEEE TRANSACTIONS ON INFORMATION THEORY*, vol. 62, no. 11, pp. 6609-6619.View/Download from: UTS OPUS or Publisher's site

Lai, CY, Hsieh, MH & Lu, HF 2016, 'On the MacWilliams Identity for Classical and Quantum Convolutional Codes', *IEEE Transactions on Communications*, vol. 64, no. 8, pp. 3148-3159.View/Download from: UTS OPUS or Publisher's site

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© 2016 IEEE. The weight generating functions associated with convolutional codes (CCs) are based on state space realizations or the weight adjacency matrices (WAMs). The MacWilliams identity for CCs on the WAMs was first established by Gluesing-Luerssen and Schneider in the case of minimal encoders, and generalized by Forney. We consider this problem in the viewpoint of constraint codes and obtain a simple and direct proof of this MacWilliams identity in the case of minimal encoders. For our purpose, we choose a different representation for the exact weight generating function (EWGF) of a block code, by defining it as a linear combination of orthonormal vectors in Dirac bra-ket notation. This representation provides great flexibility so that general split weight generating functions and their MacWilliams identities can be easily obtained from the MacWilli ams identity for EWGFs. As a result, we also obtain the MacWilliams identity for the input-parity WAMs of a systematic convolutional code and its dual. Finally, paralleling the development of the classical case, we establish the MacWilliams identity for quantum CCs.

Brun, TA, Hsieh, M-H & Perry, C 2015, 'Compatibility of state assignments and pooling of information', *PHYSICAL REVIEW A*, vol. 92, no. 1.View/Download from: UTS OPUS or Publisher's site

Hsieh, MH, Chitambar, E & Fortescue, B 2015, 'A Classical Analog to Entanglement Reversibility', *Physical Review Letters*, vol. 115, no. 9, pp. 1-5.View/Download from: UTS OPUS or Publisher's site

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In this letter we introduce the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution pXYZ and transform secret bits back into pXYZ at equal rates using local operation and public communication (LOPC). This is the classical analog to the well-studied problem of reversibly concentrating and diluting entanglement in a quantum state. We identify the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution, and it is possible that all reversible distributions have this form. These distributions are more general than what is obtained by simply constructing a classical analog to the family of quantum states known to have reversible entanglement. An indispensable tool used in our analysis is a conditional form of the G\'{a}cs-K\"{o}rner Common Information

Lee, Y-C, Liu, J, Chuang, Y-L, Hsieh, M-H & Lee, R-K 2015, 'Passive -symmetric couplers without complex optical potentials', *Physical Review A*, vol. 92, no. 5, pp. 1-4.View/Download from: UTS OPUS or Publisher's site

Brun, TA, Devetak, I & Hsieh, M-H 2014, 'Catalytic Quantum Error Correction', *IEEE Transactions on Information Theory*, vol. 60, no. 6, pp. 3073-3089.View/Download from: UTS OPUS or Publisher's site

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We develop the theory of entanglement-assisted quantum error-correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to preshared entanglement. Conventional stabilizer codes are equivalent to self-orthogonal symplectic codes. In contrast, EAQEC codes do not require self-orthogonality, which greatly simplifies their construction. We show how any classical binary or quaternary block code can be made into an EAQEC code. We provide a table of best known EAQEC codes with code length up to 10. With the self-orthogonality constraint removed, we see that the distance of an EAQEC code can be better than any standard quantum error-correcting code with the same fixed net yield. In a quantum computation setting, EAQEC codes give rise to catalytic quantum codes, which assume a subset of the qubits are noiseless. We also give an alternative construction of EAQEC codes by making classical entanglement-assisted codes coherent.

Chitambar, E & Hsieh, M-H 2014, 'Asymptotic state discrimination and a strict hierarchy in distinguishability norms', *JOURNAL OF MATHEMATICAL PHYSICS*, vol. 55, no. 11.View/Download from: UTS OPUS or Publisher's site

Chitambar, EA, Duan, R & Hsieh, M 2014, 'When Do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?', *IEEE Transactions On Information Theory*, vol. 60, no. 3, pp. 1549-1561.View/Download from: UTS OPUS or Publisher's site

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In this paper, we consider the conditions under which a given ensemble of two-qubit states can be optimally distinguished by local operations and classical communication (LOCC). We begin by completing the perfect distinguishability problem of two-qubit ensembles-both for separable operations and LOCC-by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state. Then, for the well-known task of minimum error discrimination, it is shown that almost all two-qubit ensembles consisting of three pure states cannot be optimally discriminated using LOCC. This is surprising considering that any two pure states can be distinguished optimally by LOCC. Special attention is given to ensembles that lack entanglement, and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by LOCC, thus providing new examples of the phenomenon known as non-locality without entanglement. We next consider an example of N parties who each share the same state but who are ignorant of its identity. The state is drawn from the rotationally invariant trine ensemble, and we establish a tight connection between the N-copy ensemble and Shor's lifted single-copy ensemble. For any finite N, we prove that optimal identification of the states cannot be achieved by LOCC; however, as N?8, LOCC can indeed discriminate the states optimally. This is the first result of its kind. Finally, we turn to the task of unambiguous discrimination and derive new lower bounds on the LOCC inconclusive probability for symmetric states. When applied to the double trine ensemble, this leads to a rather different distinguishability character than when the minimum error probability is considered.

Lee, Y-C, Hsieh, M-H, Flammia, ST & Lee, R-K 2014, 'Local PT symmetry violates the no-signaling principle', *Phys. Rev. Lett.*, vol. 112, no. 13.View/Download from: UTS OPUS or Publisher's site

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Bender et al. have developed PT-symmetric quantum theory as an extension of

quantum theory to non-Hermitian Hamiltonians. We show that when this model has

a local PT symmetry acting on composite systems it violates the non-signaling

principle of relativity. Since the case of global PT symmetry is known to

reduce to standard quantum mechanics, this shows that the PT-symmetric theory

is either a trivial extension or likely false as a fundamental theory.

Wilde, MM, Hsieh, M & Babar, Z 2014, 'Entanglement-Assisted Quantum Turbo Codes', *IEEE Transactions On Information Theory*, vol. 60, no. 2, pp. 1203-1222.View/Download from: UTS OPUS or Publisher's site

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An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin , in order to have the constituent decoders pass along only extrinsic information to each other rather than a posteriori probabilities as in the decoder of Poulin , and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.

Chitambar, E & Hsieh, M-H 2013, 'Revisiting the optimal detection of quantum information', *PHYSICAL REVIEW A*, vol. 88, no. 2.View/Download from: UTS OPUS or Publisher's site

Datta, N & Hsieh, M 2013, 'One-Shot Entanglement-Assisted Quantum and Classical Communication', *IEEE Transactions On Information Theory*, vol. 59, no. 3, pp. 1929-1939.View/Download from: UTS OPUS or Publisher's site

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We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analog of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario

Datta, N, Hsieh, M & Wilde, M 2013, 'Quantum Rate Distortion, Reverse Shannon Theorems, and Source-Channel Separation', *IEEE Transactions On Information Theory*, vol. 59, no. 1, pp. 615-630.View/Download from: UTS OPUS or Publisher's site

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We derive quantum counterparts of two key theorems of classical information theory, namely, the rate-distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data compression, and the source-channel separation theorem implies that a two-stage protocol consisting of compression and channel coding is optimal for transmitting a memoryless source over a memoryless channel. In spite of their importance in the classical domain, there has been surprisingly little work in these areas for quantum information theory. In this paper, we prove that the quantum rate-distortion function is given in terms of the regularized entanglement of purification. We also determine a single-letter expression for the entanglement-assisted quantum rate-distortion function, and we prove that it serves as a lower bound on the unassisted quantum rate-distortion function. This implies that the unassisted quantum rate-distortion function is nonnegative and generally not equal to the coherent information between the source and distorted output (in spite of Barnum's conjecture that the coherent information would be relevant here). Moreover, we prove several quantum source-channel separation theorems. The strongest of these are in the entanglement-assisted setting, in which we establish a necessary and sufficient condition for transmitting a memoryless source over a memoryless quantum channel up to a given distortion

Datta, N, Hsieh, M, Wilde, M & Winter, A 2013, 'Quantum-to-classical rate distortion coding', *Journal Of Mathematical Physics*, vol. 54, no. 4, pp. 1-17.View/Download from: UTS OPUS or Publisher's site

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We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit a classical description of the source, obtained by performing a measurement on it, to a receiver Bob, up to some specified level of distortion. We derive a single-letter formula for theminimum rate of classical communication needed for this task.We also evaluate this rate in the case in which Bob has some quantum side information about the source. Our results imply that, in general, Alices best strategy is a non-classical one, in which she performs a collective measurement on successive outputs of the source.

Datta, N, Mosonyi, M, Hsieh, M & Brandão, FG 2013, 'A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels', *IEEE Transactions On Information Theory*, vol. 59, no. 12, pp. 8014-8026.View/Download from: UTS OPUS or Publisher's site

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We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum hypothesis testing in terms of the smooth max-relative entropy of the two states representing the two hypotheses. Then using a relative entropy version of the quantum asymptotic equipartition property (QAEP), we can recover the strong converse rate of the i.i.d. hypothesis testing problem in the asymptotics. On the other hand, combining Stein's lemma with our bounds, we obtain a stronger ( e-independent) version of the relative entropy-QAEP. Similarly, we provide bounds on the one-shot e-error classical capacity of a quantum channel in terms of a smooth max-relative entropy variant of its Holevo capacity. Using these bounds and the e-independent version of the relative entropy-QAEP, we can recover both the Holevo- Schumacher- Westmoreland theorem about the optimal direct rate of a memoryless quantum channel with product state encoding, as well as its strong converse counterpart.

Wilde, M, Datta, N, Hsieh, M & Winter, A 2013, 'Quantum Rate-Distortion Coding With Auxiliary Resources', *IEEE Transactions On Information Theory*, vol. 59, no. 10, pp. 6755-6773.View/Download from: UTS OPUS or Publisher's site

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We extend quantum rate-distortion theory by considering auxiliary resources that might be available to a sender and receiver performing lossy quantum data compression. The first setting we consider is that of quantum rate-distortion coding with the help

Wilde, M, Hayden, P, Buscemi, F & Hsieh, M 2012, 'The information-theoretic costs of simulating quantum measurements', *Journal Of Physics A-Mathematical And General*, vol. 45, no. 45, pp. 1-67.View/Download from: UTS OPUS or Publisher's site

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Winter's measurement compression theorem stands as one of the most penetrating insights of quantum information theory. In addition to making an original and profound statement about measurement in quantum theory, it also underlies several other general protocols used for entanglement distillation and local purity distillation. The theorem provides for an asymptotic decomposition of any quantum measurement into noise and information. This decomposition leads to an optimal protocol for having a sender simulate many independent instances of a quantum measurement and send the measurement outcomes to a receiver, using as little communication as possible. The protocol assumes that the parties have access to some amount of common randomness, which is a strictly weaker resource than classical communication. In this review, we provide a second look at Winter's measurement compression theorem, detailing the information processing task, giving examples for understanding it, reviewing Winter's achievability proof, and detailing a new approach to its single-letter converse theorem. We prove an extension of the theorem to the case in which the sender is not required to receive the outcomes of the simulated measurement. The total cost of common randomness and classical communication can be lower for such a 'non-feedback' simulation, and we prove a single-letter converse theorem demonstrating optimality. We then review the DevetakâWinter theorem on classical data compression with quantum side information, providing new proofs of its achievability and converse parts. From there, we outline a new protocol that we call 'measurement compression with quantum side information,' announced previously by two of us in our work on triple trade-offs in quantum Shannon theory. This protocol has several applications, including its part in the 'classically-assisted state redistribution' protocol, which is the most general protocol on the static side of the quantum information theory tree, and ...

Wilde, MM & Hsieh, M 2012, 'Public and private resource trade-offs for a quantum channel', *Quantum Information Processing*, vol. 11, pp. 1465-1501.View/Download from: UTS OPUS or Publisher's site

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Collins and Popescu realized a powerful analogy between several resources in classical and quantum information theory. The Collins-Popescu analogy states that public classical communication, private classical communication, and secret key interact with one another somewhat similarly to the way that classical communication, quantum communication, and entanglement interact. This paper discusses the information-theoretic treatment of this analogy for the case of noisy quantum channels. We determine a capacity region for a quantum channel interacting with the noiseless resources of public classical communication, private classical communication, and secret key. We then compare this region with the classical-quantum-entanglement region from our prior efforts and explicitly observe the information-theoretic consequences of the strong correlations in entanglement and the lack of a super-dense coding protocol in the public-private-secret-key setting. The region simplifies for several realistic, physically-motivated channels such as entanglement-breaking channels, Hadamard channels, and quantum erasure channels, and we are able to compute and plot the region for several examples of these channels.

Wilde, MM & Hsieh, M 2012, 'The quantum dynamic capacity formula of a quantum channel', *Quantum Information Processing*, vol. 11, no. 6, pp. 1431-1463.View/Download from: UTS OPUS or Publisher's site

#### View description

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an ab initio approach, using only the most basic tools in the quantum information theorists toolkit: the Alicki-Fannes inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the quantum dynamic capacity formula characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula reduces the computation of the trade-off surface to a tractable, textbook problem in Pareto trade-off analysis, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.

Wilde, MM & Hsieh, MH 2012, 'Erratum: The quantum dynamic capacity formula of a quantum channel; Public and private resource trade-offs for a quantum channel (Quantum Information Processing DOI: 10.1007/s11128-011-0310-6)', *Quantum Information Processing*, vol. 11, no. 6, pp. 1503-1509.View/Download from: Publisher's site

Zhao, S-M, Xiao, Y, Zhu, Y, Zhu, X-L & Hsieh, M-H 2012, 'NEW CLASS OF QUANTUM CODES CONSTRUCTED FROM CYCLIC DIFFERENCE SET', *INTERNATIONAL JOURNAL OF QUANTUM INFORMATION*, vol. 10, no. 1.View/Download from: UTS OPUS or Publisher's site

Datta, N & Hsieh, M-H 2011, 'The apex of the family tree of protocols: optimal rates and resource inequalities', *NEW JOURNAL OF PHYSICS*, vol. 13.View/Download from: UTS OPUS or Publisher's site

Hsieh, M & Le Gall, F 2011, 'NP-hardness of decoding quantum error-correction codes', *Physical Review A*, vol. 83, no. 5, pp. 1-5.View/Download from: UTS OPUS or Publisher's site

#### View description

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.

Hsieh, M, Yen, W & Hsu, L 2011, 'High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement', *IEEE Transactions On Information Theory*, vol. 57, no. 3, pp. 1761-1769.View/Download from: UTS OPUS or Publisher's site

#### View description

Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally entangled states in constructing EAQECCs is a practical obstacle to its use. It is also conjectured that the power of entanglement-assisted formalism to convert those good classical codes comes from massive consumption of maximally entangled states. We show that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length. Notably, two families of EAQECCs constructed in the paper require only one copy of maximally entangled state no matter how large the code length is. These families of EAQECCs that are constructed from classical finite geometric LDPC codes perform very well according to our numerical simulations. Our work indicates that EAQECCs are not only theoretically interesting, but also physically implementable. Finally, these high performance entanglement-assisted LDPC codes with low entanglement consumption rates allow one to construct high-performance standard QECCs with very similar parameters.

Datta, N & Hsieh, M-H 2010, 'Universal coding for transmission of private information', *JOURNAL OF MATHEMATICAL PHYSICS*, vol. 51, no. 12.View/Download from: Publisher's site

Hsieh, M & Wilde, M 2010, 'Trading Classical Communication, Quantum Communication, and Entanglement in Quantum Shannon Theory', *IEEE Transactions On Information Theory*, vol. 56, no. 9, pp. 4507-4730.View/Download from: UTS OPUS or Publisher's site

#### View description

In this paper, we give tradeoffs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three fundamental protocols of teleportation, superdense coding, and entanglement distribution. We then provide an achievable rate region and a matching multiletter converse for the direct-static capacity theorem. This theorem applies to the scenario where a large number of copies of a noisy bipartite state are available (in addition to consumption or generation of the above three noiseless resources). Our coding strategy involves a protocol that we name the classically assisted state redistribution protocol and the three fundamental protocols. We finally provide an achievable rate region and a matching multiletter converse for the direct-dynamic capacity theorem. This theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources. Our coding strategy combines the classically enhanced father protocol with the three fundamental unit protocols.

Hsieh, M & Wilde, MM 2010, 'Entanglement-assisted communication of classical and quantum Information', *IEEE Transactions On Information Theory*, vol. 56, no. 9, pp. 4682-4704.View/Download from: UTS OPUS or Publisher's site

#### View description

We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the region are rate triples, consisting of the classical communication rate, the quantum communication rate, and the entanglement consumption rate of a particular coding scheme. The crucial protocol in achieving the boundary points of the capacity region is a protocol that we name the classically-enhanced father protocol. The classically-enhanced father protocol is more general than other protocols in the family tree of quantum Shannon theoretic protocols, in the sense that several previously known quantum protocols are now child protocols of it. The classically-enhanced father protocol also shows an improvement over a time-sharing strategy for the case of a qubit dephasing channelthis result justifies the need for simultaneous coding of classical and quantum information over an entanglement-assisted quantum channel. Our capacity theorem is of a multi-letter nature (requiring a limit over many uses of the channel), but it reduces to a singleletter characterization for at least three channels: the completely depolarizing channel, the quantum erasure channel, and the qubit dephasing channel.

Hsieh, M, Yen, W & Hsu, L 2010, 'Undetermined states: how to find them and their applications', *European Physical Journal D*, vol. 61, no. 1, pp. 261-265.View/Download from: UTS OPUS or Publisher's site

#### View description

We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.

Shih, Y, Hsieh, M & Wei, H 2010, 'Multicasting Homogeneous and Heterogeneous Quantum States in Quantum Networks', *Nano Communication Networks*, vol. 1, no. 4, pp. 273-282.View/Download from: UTS OPUS or Publisher's site

#### View description

In this paper, we target the practical implementation issues of quantum multicast networks. First, we design a recursive lossless compression that allows us to control the trade-off between the circuit complexity and the dimension of the compressed quantum state. We give a formula that describes the trade-off, and further analyze how the formula is affected by the controlling parameter of the recursive procedure. Our recursive lossless compression can be applied in a quantum multicast network where the source outputs homogeneous quantum states (many copies of a quantum state) to a set of destinations through a bottleneck. Such a recursive lossless compression is extremely useful in the current situation where the technology of producing large-scale quantum circuits is limited. Second, we develop two lossless compression schemes that work for heterogeneous quantum states (many copies of a set of quantum states) when the set of quantum states satisfies a certain structure. The heterogeneous compression schemes provide extra compressing power over the homogeneous compression scheme. Finally, we realize our heterogeneous compression schemes in several quantum multicast networks, including the single-source multi-terminal model, the multi-source multi-terminal model, and the ring networks. We then analyze the bandwidth requirements for these network models.

Hsieh, M-H & Wilde, MM 2009, 'Public and private communication with a quantum channel and a secret key', *PHYSICAL REVIEW A*, vol. 80, no. 2.View/Download from: Publisher's site

Hsieh, M-H, Brun, TA & Devetak, I 2009, 'Entanglement-assisted quantum quasicyclic low-density parity-check codes', *PHYSICAL REVIEW A*, vol. 79, no. 3.View/Download from: Publisher's site

Hsieh, M, Devetak, I & Winter, A 2008, 'Entanglement-Assisted Capacity of Quantum Multiple-Access Channels', *IEEE Transactions On Information Theory*, vol. 54, no. 7, pp. 3078-3090.View/Download from: UTS OPUS or Publisher's site

#### View description

We find a regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple access channels (QMAC). We illustrate the capacity region calculation with the example of the collective phase-flip channel which admits a single-letter characterization. On the way, we provide a first-principles proof of the EA coding theorem based on a packing argument. We observe that the Holevo-Schumacher-Westmoreland theorem may be obtained from a modification of our EA protocol. We remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver, in analogy to the two-party case. In this way, we relate several previous results regarding QMACs.

Kremsky, I, Hsieh, M-H & Brun, TA 2008, 'Classical enhancement of quantum-error-correcting codes', *PHYSICAL REVIEW A*, vol. 78, no. 1.View/Download from: Publisher's site

Hsieh, M-H, Devetak, I & Brun, T 2007, 'General entanglement-assisted quantum error-correcting codes', *PHYSICAL REVIEW A*, vol. 76, no. 6.View/Download from: Publisher's site

Brun, T, Devetak, I & Hsieh, M 2006, 'Correcting Quantum Errors with Entanglement', *Science*, vol. 314, no. 5798, pp. 436-439.View/Download from: Publisher's site

#### View description

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum errorcorrecting codes, thus allowing us to quantize all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.

Du, Y, Hsieh, M-H & Tao, D, 'Efficient Online Quantum Generative Adversarial Learning Algorithms with Applications'.

#### View description

The exploration of quantum algorithms that possess quantum advantages is a

central topic in quantum computation and quantum information processing. One

potential candidate in this area is quantum generative adversarial learning

(QuGAL), which conceptually has exponential advantages over classical

adversarial networks. However, the corresponding learning algorithm remains

obscured. In this paper, we propose the first quantum generative adversarial

learning algorithm-- the quantum multiplicative matrix weight algorithm

(QMMW)-- which enables the efficient processing of fundamental tasks. The

computational complexity of QMMW is polynomially proportional to the number of

training rounds and logarithmically proportional to the input size. The core

concept of the proposed algorithm combines QuGAL with online learning. We

exploit the implementation of QuGAL with parameterized quantum circuits, and

numerical experiments for the task of entanglement test for pure state are

provided to support our claims.

Du, Y, Hsieh, M-H, Liu, T & Tao, D, 'Implementable Quantum Classifier for Nonlinear Data'.

#### View description

In this Letter, we propose a quantum machine learning scheme for the

classification of classical nonlinear data. The main ingredients of our method

are variational quantum perceptron (VQP) and a quantum generalization of

classical ensemble learning. Our VQP employs parameterized quantum circuits to

learn a Grover search (or amplitude amplification) operation with classical

optimization, and can achieve quadratic speedup in query complexity compared to

its classical counterparts. We show how the trained VQP can be used to predict

future data with $O(1)$ {query} complexity. Ultimately, a stronger nonlinear

classifier can be established, the so-called quantum ensemble learning (QEL),

by combining a set of weak VQPs produced using a subsampling method. The

subsampling method has two significant advantages. First, all $T$ weak VQPs

employed in QEL can be trained in parallel, therefore, the query complexity of

QEL is equal to that of each weak VQP multiplied by $T$. Second, it

dramatically reduce the {runtime} complexity of encoding circuits that map

classical data to a quantum state because this dataset can be significantly

smaller than the original dataset given to QEL. This arguably provides a most

satisfactory solution to one of the most criticized issues in quantum machine

learning proposals. To conclude, we perform two numerical experiments for our

VQP and QEL, implemented by Python and pyQuil library. Our experiments show

that excellent performance can be achieved using a very small quantum circuit

size that is implementable under current quantum hardware development.

Specifically, given a nonlinear synthetic dataset with $4$ features for each

example, the trained QEL can classify the test examples that are sampled away

from the decision boundaries using $146$ single and two qubits quantum gates

with $92\%$ accuracy.

Du, Y, Hsieh, M-H, Liu, T & Tao, D, 'The Expressive Power of Parameterized Quantum Circuits'.

#### View description

Parameterized quantum circuits (PQCs) have been broadly used as a hybrid

quantum-classical machine learning scheme to accomplish generative tasks.

However, whether PQCs have better expressive power than classical generative

neural networks, such as restricted or deep Boltzmann machines, remains an open

issue. In this paper, we prove that PQCs with a simple structure already

outperform any classical neural network for generative tasks, unless the

polynomial hierarchy collapses. Our proof builds on known results from tensor

networks and quantum circuits (in particular, instantaneous quantum polynomial

circuits). In addition, PQCs equipped with ancillary qubits for post-selection

have even stronger expressive power than those without post-selection. We

employ them as an application for Bayesian learning, since it is possible to

learn prior probabilities rather than assuming they are known. We expect that

it will find many more applications in semi-supervised learning where prior

distributions are normally assumed to be unknown. Lastly, we conduct several

numerical experiments using the Rigetti Forest platform to demonstrate the

performance of the proposed Bayesian quantum circuit.

Salek, F, Anshu, A, Hsieh, M-H, Jain, R & Fonollosa, JR, 'One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information'.

#### View description

We study the communication capabilities of a quantum channel under the most

general channel model known as the one-shot model. Unlike classical channels

that can only be used to transmit classical information (bits), a quantum

channel can be used for transmission of classical information, quantum

information (qubits) and simultaneous transmission of classical and quantum

information. In this work, we investigate the one-shot capabilities of a

quantum channel for simultaneously transmitting of bits and qubits. This

problem was studied in the asymptotic regime for a memoryless channel and a

regularized characterization of the capacity region was reported. It is known

that the transmission of private classical information is closely related to

the problem of quantum information transmission. We resort to this idea and

find achievable and converse bounds on the simultaneous transmission of the

public and private classical information. then by shifting the classical

private rate to the quantum information rate, the obtained rate regions will be

translated into rate regions of thThis in turn, leads to a rate region for

simulttaneous transmission of classical and quantum information. In the case of

asymptotic i.i.d. setting, our one-shot result is evaluated to the known

results in the literature. Our main tools used in the achievability proofs are

position-based decoding and convex-split lemma.

Wang, X, Ma, Y, Hsieh, M-H & Yung, M, 'Quantum Speedup in Adaptive Boosting of Binary Classification'.

#### View description

In classical machine learning, a set of weak classifiers can be adaptively

combined to form a strong classifier for improving the overall performance, a

technique called adaptive boosting (or AdaBoost). However, constructing the

strong classifier for a large data set is typically resource consuming. Here we

propose a quantum extension of AdaBoost, demonstrating a quantum algorithm that

can output the optimal strong classifier with a quadratic speedup in the number

of queries of the weak classifiers. Our results also include a generalization

of the standard AdaBoost to the cases where the output of each classifier may

be probabilistic even for the same input. We prove that the update rules and

the query complexity of the non-deterministic classifiers are the same as those

of deterministic classifiers, which may be of independent interest to the

classical machine-learning community. Furthermore, the AdaBoost algorithm can

also be applied to data encoded in the form of quantum states; we show how the

training set can be simplified by using the tools of t-design. Our approach

describes a model of quantum machine learning where quantum speedup is achieved

in finding the optimal classifier, which can then be applied for classical

machine-learning applications.

Zhang, C, Gao, X, Hsieh, M-H, Hang, H & Tao, D, 'Matrix Infinitely Divisible Series: Tail Inequalities and Applications in Optimization'.

#### View description

In this paper, we study tail inequalities of the largest eigenvalue of a

matrix infinitely divisible (i.d.) series, which is a finite sum of fixed

matrices weighted by i.d. random variables. We obtain several types of tail

inequalities, including Bennett-type and Bernstein-type inequalities. This

allows us to further bound the expectation of the spectral norm of a matrix

i.d. series. Moreover, by developing a new lower-bound function for

$Q(s)=(s+1)\log(s+1)-s$ that appears in the Bennett-type inequality, we derive

a tighter tail inequality of the largest eigenvalue of the matrix i.d. series

than the Bernstein-type inequality when the matrix dimension is high. The

resulting lower-bound function is of independent interest and can improve any

Bennett-type concentration inequality that involves the function $Q(s)$. The

class of i.d. probability distributions is large and includes Gaussian and

Poisson distributions, among many others. Therefore, our results encompass the

existing work \cite{tropp2012user} on matrix Gaussian series as a special case.

Lastly, we show that the tail inequalities of a matrix i.d. series have

applications in several optimization problems including the chance constrained

optimization problem and the quadratic optimization problem with orthogonality

constraints.

Zhang, C, Hsieh, M-H & Tao, D, 'On Dimension-free Tail Inequalities for Sums of Random Matrices and Applications'.

#### View description

In this paper, we present a new framework to obtain tail inequalities for

sums of random matrices. Compared with existing works, our tail inequalities

have the following characteristics: 1) high feasibility--they can be used to

study the tail behavior of various matrix functions, e.g., arbitrary matrix

norms, the absolute value of the sum of the sum of the $j$ largest singular

values (resp. eigenvalues) of complex matrices (resp. Hermitian matrices); and

2) independence of matrix dimension --- they do not have the matrix-dimension

term as a product factor, and thus are suitable to the scenario of

high-dimensional or infinite-dimensional random matrices. The price we pay to

obtain these advantages is that the convergence rate of the resulting

inequalities will become slow when the number of summand random matrices is

large. We also develop the tail inequalities for matrix random series and

matrix martingale difference sequence. We also demonstrate usefulness of our

tail bounds in several fields. In compressed sensing, we employ the resulted

tail inequalities to achieve a proof of the restricted isometry property when

the measurement matrix is the sum of random matrices without any assumption on

the distributions of matrix entries. In probability theory, we derive a new

upper bound to the supreme of stochastic processes. In machine learning, we

prove new expectation bounds of sums of random matrices matrix and obtain

matrix approximation schemes via random sampling. In quantum information, we

show a new analysis relating to the fractional cover number of quantum

hypergraphs. In theoretical computer science, we obtain randomness-efficient

samplers using matrix expander graphs that can be efficiently implemented in

time without dependence on matrix dimensions.

Brun, T & Hsieh, M 2013, 'Entanglement-Assisted Quantum Error-Correcting Codes' in Lidar, D & Brun, T (eds), *Quantum Error Correction*, Cambridge University Press, US, pp. 181-200.

#### View description

Quantum error-correcting codes (QECCs) have turned out to have many applications; but their primary purpose, of course, is to protect quantum information from noise. This need manifests itself in two rather different situations. The first is in quantum computing. The qubits in a quantum computer are subject to noise due both to imprecision in the operations (or gates) and to interactions with the external environment. They undergo errors when they are acted upon, and when they are just being stored (though hopefully not at the same rate). All the qubits in the computer must be kept error-free long enough for the computation to be completed. This is the principle of fault tolerance. A rather different situation occurs in quantum communication. Here, the sender and receiver (Alice and Bob) are assumed to be physically separated, and the qubits travel from the sender to the receiver over a (presumably noisy) channel. This channel is assumed to be the dominant source of errors. While the qubits may undergo processing before and after transmission, errors during this processing are considered negligible compared to the channel errors. This picture of transmission through a channel is similar in spirit to the paradigm underlying much of classical information theory.

Cheng, HC, Hanson, EP, Datta, N & Hsieh, MH 2018, 'Error Exponents and Strong Converse Exponents for Classical Data Compression with Quantum Side Information', *IEEE International Symposium on Information Theory - Proceedings*, IEEE International Symposium on Information Theory, IEEE, Vail, CO, USA, pp. 2162-2166.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2018 IEEE. In this paper, we analyze classical data compression with quantum side information (also known as the classical-quantum Slepian- Wolf protocol) in the so-called large and moderate deviation regimes. In the non-asymptotic setting, the protocol involves compressing classical sequences of finite length n and decoding them with the assistance of quantum side information. In the large deviation regime, the compression rate is fixed, and we obtain bounds on the error exponent function, which characterizes the minimal probability of error as a function of the rate. Devetak and Winter showed that the asymptotic data compression limit for this protocol is given by a conditional entropy. For any protocol with a rate below this quantity, the probability of error converges to one asymptotically and its speed of convergence is given by the strong converse exponent function. We obtain finite blocklength bounds on this function, and determine exactly its asymptotic value, thus improving on previous results by Tomamichel. In the moderate deviation regime for the compression rate, the latter is no longer considered to be fixed. It is allowed to depend on the blocklength n, but assumed to decay slowly to the asymptotic data compression limit. Starting from a rate above this limit, we determine the speed of convergence of the error probability to zero and show that it is given in terms of the conditional information variance. Our results complement earlier results obtained by Tomamichel and Hayashi, in which they analyzed the so-called small deviation regime of this protocol.

Fan, J, Hsieh, MH, Chen, H, Chen, H & Li, Y 2018, 'Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors', *IEEE International Symposium on Information Theory - Proceedings*, IEEE International Symposium on Information Theory, IEEE, Vail, CO, USA, pp. 2336-2340.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2018 IEEE. In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.

Salek, F, Anshu, A, Hsieh, MH, Jain, R & Fonollosa, JR 2018, 'One-shot Capacity Bounds on the Simultaneous Transmission of Public and Private Information over Quantum Channels', *IEEE International Symposium on Information Theory - Proceedings*, IEEE International Symposium on Information Theory, IEEE, Vail, CO, USA, pp. 296-300.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2018 IEEE. We aim to study the optimal rates of transmission of public and private classical information over a quantum channel in the most general channel model. To this end, we discuss a scenario in which a quantum channel is being used only once, i.e., one-shot regime is considered. A quantum channel can be used to send classical information (bits) either publicly or privately and for either case, one-shot bounds have been reported in the literature. This paper investigates the one-shot capacity capabilities of a quantum channel for simultaneous transmission of public and private information. We derive an achievable rate region in the form of a tradeoff between public and private rates. We also provide converse bounds assessing the " of our achievable rates. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

Cheng, HC & Hsieh, MH 2017, 'Moderate deviations for classical-quantum channels', *IEEE International Symposium on Information Theory - Proceedings*, IEEE International Symposium on Information Theory, IEEE, Aachen, Germany, pp. 296-300.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2017 IEEE. "To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award." We show that the reliable communication through a classical-quantum channel is possible when the transmission rate approaches the channel capacity sufficiently slowly. This scenario exists between the non-vanishing error probability regime, where the rate tends to capacity with a fixed error, and the small error probability regime, where the error vanishes given a rate below capacity. The proof employs a sharp concentration bound in strong large deviation theory, and the asymptotic expansions of the error-exponent functions.

Cheng, HC & Hsieh, MH 2017, 'Moderate deviations for quantum hypothesis testing and a martingale inequality', *2017 IEEE International Symposium on Information Theory (ISIT)*, International Symposium on Information Theory, IEEE, Aachen, Germany, pp. 1978-1982.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2017 IEEE. 'To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.' We study the asymptotic behavior of the type-I error in quantum hypothesis testing when the exponent of the type-II error approaches the quantum relative entropy sufficiently slowly. Our result shows that the moderate deviation principle holds for the testing problem if the quantum relative variance is positive. Our proof strategy employs strong large deviation theory and a martingale inequality.

Cheng, HC, Hsieh, MH & Tomamichel, M 2017, 'Sphere-packing bound for classical-quantum channels', *IEEE International Symposium on Information Theory - Proceedings*, IEEE Information Theory Workshop, IEEE, Kaohsiung, Taiwan, pp. 479-483.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2017 IEEE. We study lower bounds on the optimal error probability in channel coding at rates below capacity, commonly termed sphere-packing bounds. In this work, we establish a sphere-packing bound for classical-quantum channels, which significantly improves previous prefactor from the order of subexponential to polynomial. Furthermore, the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes in the order of o(log n/n), indicating our sphere-packing bound is almost exact in the high rate regime. The main technical contributions are two converse Hoeffding bounds for quantum hypothesis testing and the saddle-point properties of error exponent functions.

Cheng, HC, Hsieh, MH & Tomamichel, M 2017, 'Sphere-packing bound for symmetric classical-quantum channels', *IEEE International Symposium on Information Theory - Proceedings*, IEEE International Symposium on Information Theory, IEEE, Aachen, Germany, pp. 286-290.View/Download from: UTS OPUS or Publisher's site

#### View description

© 2017 IEEE. "To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award." We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial, This established pre-factor is arguably optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function.

Chitambar, E, Fortescue, B & Hsieh, MH 2015, 'Distributions attaining secret key at a rate of the conditional mutual information', *Advances in Cryptology - CRYPTO 2015: 35th Annual Cryptology Conference Santa Barbara, CA, USA, August 16–20, 2015 Proceedings, Part II*, Annual International Cryptology Conference, SPRINGER-VERLAG BERLIN, Santa Barbara, CA, pp. 443-462.View/Download from: UTS OPUS or Publisher's site

#### View description

© International Association for Cryptologic Research 2015. In this paper we consider the problem of extracting secret key from an eavesdropped source pXY Z at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice (X) and Bob (Y) are unable to communicate but share common randomness with the eavesdropper Eve (Z), (ii) Alice and Bob are allowed one-way public communication, and (iii) Alice and Bob are allowed two-way public communication. Distributions having a key rate of the conditional mutual information are precisely those in which a 'helping' Eve offers Alice and Bob no greater advantage for obtaining secret key than a fully adversarial one. For each of the above scenarios, strong necessary conditions are derived on the structure of distributions attaining a secret key rate of I(X: Y |Z). In obtaining our results, we completely solve the problem of secret key distillation under scenario (i) and identify H(S|Z) to be the optimal key rate using shared randomness, where S is the Gàcs-Körner Common Information. We thus provide an operational interpretation of the conditional Gàcs- Körner Common Information. Additionally, we introduce simple example distributions in which the rate I(X: Y |Z) is achievable if and only if two-way communication is allowed.

Hsieh, M & Watanabe, S 2015, 'Fully quantum source compression with a quantum helper', *Proceedings of the 2015 IEEE Information Theory Workshop - Fall (ITW)*, Information Theory Workshop, IEEE, Jeju, pp. 307-311.View/Download from: UTS OPUS or Publisher's site

#### View description

We study source compression with a helper in the

fully quantum regime, extending our earlier result on classical

source compression with a quantum helper [arXiv:1501.04366,

2015]. We characterise the quantum resources involved in this

problem, and derive a single-letter expression of the achievable

rate region when entanglement assistance is available. The direct

coding proof is based on a combination of two fundamental

protocols, namely the quantum state merging protocol and

the quantum reverse Shannon theorem (QRST). This result

connects distributed source compression with the QRST protocol,

a quantum protocol that consumes noiseless resources to simulate

a noisy quantum channel.

Hsieh, M & Watanabe, S 2015, 'Source Compression with a Quantum Helper', *Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)*, IEEE International Symposium on Information Theory, IEEE, Hong Kong, pp. 2762-2766.View/Download from: UTS OPUS or Publisher's site

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We study classical source coding with quantum side-information where the quantum side-information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct part of our result is proved via the measurement compression theory by Winter. Our result reveals that a helper's scheme that separately conducts a measurement and a compression is suboptimal, and the measurement compression is fundamentally needed to achieve the optimal rate region.

Lai, C & Hsieh, MH 2014, 'The MacWilliams identity for quantum convolutional codes', *2014 IEEE International Symposium on Information Theory (ISIT)*, IEEE International Symposium on Information Theory, IEEE, Honolulu, HI, pp. 911-915.View/Download from: UTS OPUS or Publisher's site

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In this paper, we propose a definition of the dual code of a quantum convolutional code, with or without entanglement assistance. We then derive a MacWilliams identity for quantum convolutional codes. Along the way, we obtain a direct proof of the MacWilliams identity, first found by Gluesing-Luerssen and Schneider, in the setting of classical convolutional codes.

Lai, CY, Hsieh, M & Lu, HF 2014, 'A Complete MacWilliams Theorem for Convolutional Codes', *2014 IEEE Information Theory Workshop, ITW 2014*, Information Theory Workshop, IEEE, Hobart, TAS, pp. 157-161.View/Download from: UTS OPUS or Publisher's site

Datta, N, Hsieh, M & Wilde, MM 2011, 'Quantum rate distortion, reverse Shannon theorems, and source-channel', The 14th workshop on Quantum Information Processing (QIP 2012), Montreal, Canada.

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We derive quantum counterparts of two key theorems of classical information theory, namely, the rate distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data compression, and the source-channel separation theorem implies that a two-stage protocol consisting of compression and channel coding is optimal for transmitting a memoryless source over a memoryless channel. In spite of their importance in the classical domain, there has been surprisingly little work in these areas for quantum information theory. In the present paper, we prove that the quantum rate distortion function is given in terms of the regularized entanglement of purification. We also determine a single-letter expression for the entanglement-assisted quantum rate distortion function, and we prove that it serves as a lower bound on the unassisted quantum rate distortion function. This implies that the unassisted quantum rate distortion function is non-negative and generally not equal to the coherent information between the source and distorted output (in spite of Barnum's conjecture that the coherent information would be relevant here). Moreover, we prove several quantum source-channel separation theorems. The strongest of these are in the entanglement-assisted setting, in which we establish a necessary and sufficient codition for transmitting a memoryless source over a memoryless quantum channel up to a given distortion.

Hsieh, M 2012, 'Introduction to Quantum Information Theory', Quantum Physics of Information, Shanghai Jiao Tong University, Shanghai, China.

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The building blocks of our communication systems and computational devices are bits. The scope of quantum information science is to replace bits with âqubitsâ, objects that obey the laws of quantum physics. This is a great challenge that has the potential to revolutionize information technology.The event will consist of a school and a workshop: the school will expose the attendants to the basic concepts of quantum information and computation,and it will be a great occasion for newcomers to the field. The workshop will comprise advanced tutorials and a program of talks based on current research problems and results.

Hsieh, M 2012, 'Strong converse capacities of quantum channels for classical information', Japan-Singapore Workshop on Multi-user Quantum Networks, Singapore.

Hsieh, M 2012, 'The information-theoretic costs of simulating quantum measurements', International Workshop on Quantum Computing and Quantum Information Processing 2012, Chinese Academy of Sciences (CAS), Beijing, China.

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This workshop will focus on the recent advances in quantum computing and quantum information processing. It aims at providing a forum for international and Chinese researchers in these fields to exchange their latest research results.

Fujiwara, Y & Hsieh, M 2011, 'Adaptively correcting quantum errors with entanglement', *2011 IEEE International Symposium on Information Theory Proceedings (ISIT)*, IEEE International Symposium on Information Theory, IEEE, St Petersburg, pp. 279-283.View/Download from: UTS OPUS or Publisher's site

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Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we develop a new kind of error-correcting protocol which can flexibly trade error correction abilities between the two types of errors, such that high error correction performance is achieved both in symmetric and in asymmetric situations. The characteristics of the QECCs can be optimized in an adaptive manner during information transmission. The proposed entanglement-assisted QECCs require only one ebit regardless of the degree of asymmetry at a given moment and can be decoded in polynomial time.

Wilde, MM & Hsieh, MH 2011, 'Entanglement boosts quantum turbo codes', *IEEE International Symposium on Information Theory - Proceedings*, IEEE International Symposium on Information Theory, IEEE, St. Petersburg, Russia, pp. 445-449.View/Download from: UTS OPUS or Publisher's site

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One of the unexpected breakdowns in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for a quantum turbo code to have an unbounded minimum distance and for its iterative decoding algorithm to converge, respectively. Here, we show that the entanglement- assisted paradigm gives a theoretical and simulated turbo boost to these codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties, and simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 5.5 dB beyond that of standard quantum turbo codes. Entanglement is the resource that enables a convolutional encoder to satisfy both properties because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them. Simulation results demonstrate that interleaved serial concatenation of EAQ convolutional encoders leads to a powerful code construction with excellent performance on a memoryless depolarizing channel. © 2011 IEEE.

Wilde, M & Hsieh, M 2010, 'Entanglement generation with a quantum channel and a shared state', *2010 IEEE International Symposium onInformation Theory Proceedings (ISIT)*, IEEE International Symposium onInformation Theory Proceedings, IEEE, Austin, USA, pp. 2713-2717.View/Download from: UTS OPUS or Publisher's site

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We introduce a new protocol, the channel-state coding protocol, to quantum Shannon theory. This protocol generates entanglement between a sender and receiver by coding for a noisy quantum channel with the aid of a noisy shared state. The mother and father protocols arise as special cases of the channel-state coding protocol, where the channel is noiseless or the state is a noiseless maximally entangled state, respectively. The channel-state coding protocol paves the way for formulating entanglement-assisted quantum error-correcting codes that are robust to noise in shared entanglement. Finally, the channel-state coding protocol leads to a Smith-Yard superactivation, where we can generate entanglement using a zero-capacity erasure channel and a non-distillable bound entangled state.

Wilde, MM & Hsieh, M 2010, 'Trading Resources in Quantum Communication', The 10th Asian Conference on Quantum Information Science (AQIS10), Tokyo, Japan.

Devetak, I, Brun, T & Hsieh, M 2006, 'Entanglement-assisted quantum error-correcting code', *New Trends in Mathematical Physics: Selected Contributions of the XVth International Congress on Mathematical Physics*, International Congress on Mathematical Physics, Springer, Rio de Janeiro, Brazil, pp. 161-172.View/Download from: Publisher's site

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We develop the theory of entanglement-assisted quantum error correcting codes (EAQECCs), a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional stabilizer codes are equivalent to self-orthogonal symplectic codes. In contrast, EAQECCs do not require self-orthogonality, which greatly simplifies their construction. We show how any classical quaternary block code can be made into a EAQECC. Furthermore, the error-correcting power of the quantum codes follows directly from the power of the classical codes.

Hsieh, M, Yen, W & Hsu, L 2009, 'Performance of Entanglement-assisted Quantum LDPC Codes', *The 21th Quantum Information Technology Symposium (QIT21)*, The University of Electro-Communications, Japan.

Hsieh, M-H & Wilde, MM 2009, 'Optimal Trading of Classical Communication, Quantum Communication, and Entanglement', *THEORY OF QUANTUM COMPUTATION, COMMUNICATION, AND CRYPTOGRAPHY*, 4th Workshop on Theory of Quantum Computation, Communication and Cryptography, SPRINGER-VERLAG BERLIN, Waterloo, CANADA, pp. 85-+.

Wilde, MM & Hsieh, M 2009, 'Superactive entanglement generation with a zero-capacity quantum channel and a non-distillable shared state', *The 9th Asian Conference on Quantum Information Science (AQIS09)*, Nanjing, China.

Hsieh, M, Luo, Z & Brun, T 2008, 'Secret keys assisted private classical communication capacity over quantum channels', The 8th Asian Conference on Quantum Information Science (AQIS08), Seoul, Korea.

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We prove a regularized formula for the secret key-assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity \cite{DHW05RI}. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes private classical communication \it{without} secret key assistance as a child protocol.

Brun, T, Devetak, I & Hsieh, M 2007, 'General entanglement-assisted quantum error-correcting codes', *IEEE International Symposium on Information Theory*, IEEE International Symposium on Information Theory, IEEE, Nice, France, pp. 2101-2105.View/Download from: UTS OPUS or Publisher's site

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Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.

Brun, T, Devetak, I & Hsieh, M 2007, 'Quantum quasi-cyclic low-density parity-check codes', *The 7th Asian Conference on Quantum Information Science (AQIS07)*, Shiran Kaikan, Kyoto University, Japan.

Brun, T, Devetak, I & Hsieh, M 2006, 'Entanglement-assisted quantum error correction', *The 6th Asian Conference on Quantum Information Science (AQIS06)*, BeiJing, China.

Hsieh, M & Chen, K-C 2002, 'A novel channel interference identification', *Vehicular Technology Conference, 2002. VTC Spring 2002. IEEE 55th*, IEEE Vehicular Technology Conference, IEEE, Birmingham, Alabama, pp. 1886-1890.View/Download from: Publisher's site

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Both direct sequence and frequency hopping spread spectrum communication systems co-exist in the unlicensed band such as 2.4 GHz ISM band. We propose a novel structure to obtain the channel information so that more robust communication is possible. Both theoretical and numerical results are presented to demonstrate effectiveness.

Cheng, H-C, Hsieh, M-H & Tomamichel, M 2019, 'Quantum Sphere-Packing Bounds With Polynomial Prefactors'.

Anshu, A, Hsieh, M-H & Jain, R 2018, 'Noisy quantum state redistribution with promise and the Alpha-bit'.

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We consider a variation of the well-studied quantum state redistribution

task, in which the starting state is known only to the receiver Bob and not to

the sender Alice. We refer to this as quantum state redistribution with a

one-sided promise. In addition, we consider communication from Alice to Bob

over a noisy channel $\mathcal{N}$, instead of the noiseless channel, as is

usually considered in state redistribution. We take a natural approach towards

solution of this problem where we "embed" the promise as part of the state and

then invoke known protocols for quantum state redistribution composed with

known protocols for transfer of quantum information over noisy channels. We

interpret the communication primitive Alpha-bit, recently introduced in Ref.

[arXiv:1706.09434], as an instance of state transfer (a sub-task of state

redistribution) with a one-sided promise over noisy channels. Using our

approach, we are able to reproduce the Alpha-bit capacities with or without

entanglement assistance in Ref. [arXiv:1706.09434], using known protocols for

quantum state redistribution and quantum communication over noisy channels.

Furthermore, we generalize the entanglement assisted classical capacity of the

Alpha-bit, showing that any quantum state redistribution protocol can be used

as a black box to simulate classical communication.

Cheng, H-C, Hanson, EP, Datta, N & Hsieh, M-H 2018, 'Non-Asymptotic Classical Data Compression with Quantum Side Information'.

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In this paper, we analyze classical data compression with quantum side

information (also known as the classical-quantum Slepian-Wolf protocol) in the

so-called large and moderate deviation regimes. In the non-asymptotic setting,

the protocol involves compressing classical sequences of finite length $n$ and

decoding them with the assistance of quantum side information. In the large

deviation regime, the compression rate is fixed, and we obtain bounds on the

error exponent function, which characterizes the minimal probability of error

as a function of the rate. Devetak and Winter showed that the asymptotic data

compression limit for this protocol is given by a conditional entropy. For any

protocol with a rate below this quantity, the probability of error converges to

one asymptotically and its speed of convergence is given by the strong converse

exponent function. We obtain finite blocklength bounds on this function, and

determine exactly its asymptotic value. In the moderate deviation regime for

the compression rate, the latter is no longer considered to be fixed. It is

allowed to depend on the blocklength $n$, but assumed to decay slowly to the

asymptotic data compression limit. Starting from a rate above this limit, we

determine the speed of convergence of the error probability to zero and show

that it is given in terms of the conditional information variance. Our results

complement earlier results obtained by Tomamichel and Hayashi, in which they

analyzed the so-called small deviation regime of this protocol.

Luo, Y, Li, Y & Hsieh, M-H 2018, 'Inequivalent Multipartite Coherence Classes and New Coherence Monotones'.

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Quantum coherence has received significant attention in recent years, but its

study is mostly conducted in single party settings. In this paper, we

generalize important results in multipartite entanglement theory to their

counterparts in quantum coherence theory. First, we give a necessary and

sufficient condition for when two pure multipartite states are equivalent under

local quantum incoherent operations and classical communication (LICC), i.e.,

two states can be deterministically transformed to each other under LICC

operations. Next, we investigate and give the conditions in which such a

transformation succeeds only stochastically. Lastly, we introduce two coherence

monotones: accessible coherence and source coherence, following the logistics

given in [\emph{Phys. Rev. Lett. 115, 150502 (2015)}]. These coherence

monotones have a straightforward operational interpretation, namely, the

accessible coherence characterizes the proficiency of a state to generate other

states via quantum incoherent operations, while the source coherence

characterizes the set of states that can be reached via quantum incoherent

operations acting on the given state of interest.

Anshu, A, Hsieh, M-H & Jain, R 2017, 'Quantifying resource in catalytic resource theory'.

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We consider a general resource theory that allows the use of free resource as

a catalyst. We show that the amount of `resource' contained in a given state,

in the asymptotic scenario, is equal to the regularized relative entropy of

resource of that state, which then yields a straightforward operational meaning

to this quantity. Such an answer has been long sought for in any resource

theory since the usefulness of a state in information-processing tasks is

directly related to the amount of resource the state possesses in the

beginning. While we need to place a few assumptions in our resource theoretical

framework, it is still general enough and includes quantum resource theory of

entanglement, coherence, asymmetry, non-uniformity, purity, contextuality,

stabilizer computation and the classical resource theory of randomness

extraction as special cases. Since our resource theoretic framework includes

entanglement theory, our result also implies that the amount of noise one has

to inject locally in order to erase all entanglement contained in an entangled

state is equal to the regularized relative entropy of entanglement, resolving

an open question posted in [Groisman et al., Phys. Rev. A. 72: 032317, 2005].

On the way to prove the main result, we also quantify the amount of resource

contained in a state in the one-shot setting (where one only has a single copy

of the state), in terms of the smooth max-relative entropy. Our one-shot result

employs a recently developed technique of convex-split lemma.

Zhu, EY, Zhuang, Q, Hsieh, M-H & Shor, PW 2017, 'Superadditivity in trade-off capacities of quantum channels'.

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In this article, we investigate the additivity phenomenon in the dynamic

capacity of a quantum channel for trading classical communication, quantum

communication and entanglement. Understanding such additivity property is

important if we want to optimally use a quantum channel for general

communication purpose. However, in a lot of cases, the channel one will be

using only has an additive single or double resource capacity, and it is

largely unknown if this could lead to an superadditive double or triple

resource capacity. For example, if a channel has an additive classical and

quantum capacity, can the classical-quantum capacity be superadditive? In this

work, we answer such questions affirmatively.

We give proof-of-principle requirements for these channels to exist. In most

cases, we can provide an explicit construction of these quantum channels. The

existence of these superadditive phenomena is surprising in contrast to the

result that the additivity of both classical-entanglement and classical-quantum

capacity regions imply the additivity of the triple capacity region.

Cheng, H-C & Hsieh, M-H 2015, 'New Characterizations of Matrix $Φ$-Entropies, Poincaré and Sobolev Inequalities and an Upper Bound to Holevo Quantity'.

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We derive new characterizations of the matrix $\Phi$-entropies introduced in

[Electron.~J.~Probab., 19(20): 1--30, 2014}]. These characterizations help to

better understand the properties of matrix $\Phi$-entropies, and are a powerful

tool for establishing matrix concentration inequalities for matrix-valued

functions of independent random variables. In particular, we use the

subadditivity property to prove a Poincar\'e inequality for the matrix

$\Phi$-entropies. We also provide a new proof for the matrix Efron-Stein

inequality. Furthermore, we derive logarithmic Sobolev inequalities for

matrix-valued functions defined on Boolean hypercubes and with Gaussian

distributions. Our proof relies on the powerful matrix Bonami-Beckner

inequality. Finally, the Holevo quantity in quantum information theory is

closely related to the matrix $\Phi$-entropies. This allows us to upper bound

the Holevo quantity of a classical-quantum ensemble that undergoes a special

Markov evolution.

Cheng, H-C, Hsieh, M-H & Yeh, P-C 2015, 'The Learnability of Unknown Quantum Measurements'.

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Quantum machine learning has received significant attention in recent years,

and promising progress has been made in the development of quantum algorithms

to speed up traditional machine learning tasks. In this work, however, we focus

on investigating the information-theoretic upper bounds of sample complexity -

how many training samples are sufficient to predict the future behaviour of an

unknown target function. This kind of problem is, arguably, one of the most

fundamental problems in statistical learning theory and the bounds for

practical settings can be completely characterised by a simple measure of

complexity.

Our main result in the paper is that, for learning an unknown quantum

measurement, the upper bound, given by the fat-shattering dimension, is

linearly proportional to the dimension of the underlying Hilbert space.

Learning an unknown quantum state becomes a dual problem to ours, and as a

byproduct, we can recover Aaronson's famous result [Proc. R. Soc. A

463:3089-3144 (2007)] solely using a classical machine learning technique. In

addition, other famous complexity measures like covering numbers and Rademacher

complexities are derived explicitly. We are able to connect measures of sample

complexity with various areas in quantum information science, e.g. quantum

state/measurement tomography, quantum state discrimination and quantum random

access codes, which may be of independent interest. Lastly, with the assistance

of general Bloch-sphere representation, we show that learning quantum

measurements/states can be mathematically formulated as a neural network.

Consequently, classical ML algorithms can be applied to efficiently accomplish

the two quantum learning tasks.

Cheong, KY, Hsieh, M-H & Koshiba, T 2010, 'A Weak Quantum Oblivious Transfer'.

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Due to the commonly known impossibility results, information theoretic

security is considered impossible for oblivious transfer (OT) in both the

classical and the quantum world. In this paper, we proposed a weak version of

the all-or-nothing OT. In our protocol the honest parties do not need long term

quantum memory, entanglements, or sophisticated quantum computations. We

observe some difference between the classical and quantum OT impossibilities.

Hsieh, M-H 2008, 'Entanglement-assisted Coding Theory'.

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In this dissertation, I present a general method for studying quantum error

correction codes (QECCs). This method not only provides us an intuitive way of

understanding QECCs, but also leads to several extensions of standard QECCs,

including the operator quantum error correction (OQECC), the

entanglement-assisted quantum error correction (EAQECC). Furthermore, we can

combine both OQECC and EAQECC into a unified formalism, the

entanglement-assisted operator formalism. This provides great flexibility of

designing QECCs for different applications. Finally, I show that the

performance of quantum low-density parity-check codes will be largely improved

using entanglement-assisted formalism.

Zhang, C, Hsieh, M-H & Tao, D, 'Generalization Bounds for Vicinal Risk Minimization Principle'.

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The vicinal risk minimization (VRM) principle, first proposed by

\citet{vapnik1999nature}, is an empirical risk minimization (ERM) variant that

replaces Dirac masses with vicinal functions. Although there is strong

numerical evidence showing that VRM outperforms ERM if appropriate vicinal

functions are chosen, a comprehensive theoretical understanding of VRM is still

lacking. In this paper, we study the generalization bounds for VRM. Our results

support Vapnik's original arguments and additionally provide deeper insights

into VRM. First, we prove that the complexity of function classes convolving

with vicinal functions can be controlled by that of the original function

classes under the assumption that the function class is composed of

Lipschitz-continuous functions. Then, the resulting generalization bounds for

VRM suggest that the generalization performance of VRM is also effected by the

choice of vicinity function and the quality of function classes. These findings

can be used to examine whether the choice of vicinal function is appropriate

for the VRM-based learning setting. Finally, we provide a theoretical

explanation for existing VRM models, e.g., uniform distribution-based models,

Gaussian distribution-based models, and mixup models.