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Associate Professor Min-Hsiu Hsieh

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).

Future Fellow and Associate Professor, A/DRsch Centre for Quantum Software and Information
Core Member, Centre for Quantum Software and Information
PHD
 
Phone
+61 2 9514 4494

Research Interests

My research interests include general topics in quantum information and computation.
Can supervise: Yes

Chapters

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.
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.

Conferences

Chitambar, E., Fortescue, B. & Hsieh, M.H. 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 Cryptology Conference, Santa Barbara, CA, pp. 443-462.
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© 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), 2015 IEEE Information Theory Workshop - Fall (ITW), IEEE, Jeju, pp. 307-311.
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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', 2015 IEEE International Symposium on Information Theory (ISIT), 2015 IEEE International Symposium on Information Theory, Hong Kong.
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Lai, C. & Hsieh, M.H. 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.
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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, C.Y., Hsieh, M. & Lu, H.F. 2014, 'A Complete MacWilliams Theorem for Convolutional Codes', 2014 IEEE Information Theory Workshop (ITW), IEEE, Hobart, TAS, pp. 157-161.
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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.
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.
Hsieh, M. 2012, 'Strong converse capacities of quantum channels for classical information', Japan-Singapore Workshop on Multi-user Quantum Networks, Singapore.
Hsieh, M. 2012, 'Introduction to Quantum Information Theory', Quantum Physics of Information, Shanghai Jiao Tong University, Shanghai, China.
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.
Datta, N., Hsieh, M. & Wilde, M.M. 2011, 'Quantum rate distortion, reverse Shannon theorems, and source-channel', The 14th workshop on Quantum Information Processing (QIP 2012), Montreal, Canada.
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.
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.
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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, M.M. & Hsieh, M.H. 2011, 'Entanglement boosts quantum turbo codes', IEEE International Symposium on Information Theory - Proceedings, pp. 445-449.
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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.
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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, M.M. & 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.
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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.
Wilde, M.M. & 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.
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.
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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.
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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.

Journal articles

Datta, N., Pautrat, Y. & Rouze, C. 2017, 'Contractivity properties of a quantum diffusion semigroup', JOURNAL OF MATHEMATICAL PHYSICS, vol. 58, no. 1.
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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.
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© 2016 IEEE. In this paper, we consider the problem of generating arbitrary three-party correlations from a combination of public and secret correlations. Two parties - called Alice and Bob - share perfectly correlated bits that are secret from a collaborating third party, Charlie. At the same time, all three parties have access to a separate source of correlated bits, and their goal is to convert these two resources into multiple copies of some given tripartite distribution (XYZ). We obtain a single-letter characterization of the tradeoff between public and private bits that are needed to achieve this task. The rate of private bits is shown to generalize Wyner's classic notion of common information held between a pair of random variables. The problem we consider can be contrasted fruitfully with the task of secrecy formation, in which (XYZ) is generated using public communication and local randomness but with Charlie functioning as an adversary instead of a collaborator. We describe in detail the differences between the collaborative and adversarial scenarios.
Cheng, H.C., Hsieh, M.H. & Yeh, P.C. 2016, 'The learnability of unknown quantum measurements', Quantum Information and Computation, vol. 16, no. 7-8, pp. 615-656.
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© Rinton Press. In this work, we provide an elegant framework to analyze learning matrices in the Schatten class by taking advantage of a recently developed methodology—matrix concentration inequalities. We establish the fat-shattering dimension, Rademacher/Gaussian complexity, and the entropy number of learning bounded operators and trace class operators. By characterising the tasks of learning quantum states and two-outcome quantum measurements into learning matrices in the Schatten-1 and classes, our proposed approach directly solves the sample complexity problems of learning quantum states and quantum measurements. 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/Gaussian complexities are derived explicitly under the same framework. 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.
Cheng, H.C. & Hsieh, M.H. 2016, 'Characterizations of matrix and operator-valued -entropies, and operator Efron-Stein inequalities', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 472, no. 2187.
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© 2016 The Author(s). We derive new characterizations of the matrix -entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix -entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix -entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued -entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality.
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.
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State redistribution is the protocol in which given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement.We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.
Chitambar, E. & Hsieh, M.H. 2016, 'Relating the Resource Theories of Entanglement and Quantum Coherence', Physical Review Letters, vol. 117, no. 2.
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© 2016 American Physical Society. Quantum coherence and quantum entanglement represent two fundamental features of nonclassical systems that can each be characterized within an operational resource theory. In this Letter, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically, we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations without classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the well-known Horodecki criterion for distillability.
Lai, C.Y., Hsieh, M.H. & Lu, H.F. 2016, 'On the MacWilliams Identity for Classical and Quantum Convolutional Codes', IEEE Transactions on Communications, vol. 64, no. 8, pp. 3148-3159.
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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.
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© 2016 IEEE. The auxiliary function of a classical channel appears in two fundamental quantities, the random coding exponent and the sphere-packing exponent, which yield upper and lower bounds on the error probability of decoding, respectively. A crucial property of the auxiliary function is its concavity, and this property consequently leads to several important results in finite blocklength analysis. In this paper, we prove that the auxiliary function of a classical-quantum channel also enjoys the same concavity property, extending an earlier partial result to its full generality. We also prove that the auxiliary function satisfies the data-processing inequality, among various other important properties. Furthermore, we show that the concavity property of the auxiliary function enables a geometric interpretation of the random coding exponent and the sphere-packing exponent of a classical-quantum channel. The key component in our proof is an important result from the theory of matrix geometric means.
Hsieh, M.H. & Watanabe, S. 2016, 'Channel Simulation and Coded Source Compression', IEEE Transactions on Information Theory, vol. 62, no. 11, pp. 6609-6619.
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© 2016 IEEE. Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This letter treats and solves the corresponding quantum coded source compression through an observation that connects coded source compression with channel simulation. First, we consider 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 coding theorem of our result is proved via the measurement compression theory of Winter, a quantum-to-classical channel simulation. Our result reveals that a helper's scheme which separately conducts a measurement and a compression is suboptimal, and measurement compression seems necessary to achieve the optimal rate region. We then study coded source compression in the fully quantum regime, where two different scenarios are considered depending on the types of communication channels between the legitimate source and the receiver. We further allow entanglement assistance from the quantum helper in both scenarios. We characterize the involved quantum resources and derive single-letter expressions of the achievable rate region. The direct coding proofs are based on well-known quantum protocols, the quantum state merging protocol, and the fully quantum Slepian-Wolf protocol, together with the quantum reverse Shannon theorem.
Beigi, S., Datta, N. & Leditzky, F. 2016, 'Decoding quantum information via the Petz recovery map', Journal of Mathematical Physics, vol. 57, no. 8, pp. 082203-082203.
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Leditzky, F., Wilde, M.M. & Datta, N. 2016, 'Strong converse theorems using Rényi entropies', Journal of Mathematical Physics, vol. 57, no. 8, pp. 082202-082202.
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Datta, N., Pautrat, Y. & Rouzé, C. 2016, 'Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d.—quantum lattice systems and more', Journal of Mathematical Physics, vol. 57, no. 6, pp. 062207-062207.
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Audenaert, K., Datta, N. & Ozols, M. 2016, 'Entropy power inequalities for qudits', Journal of Mathematical Physics, vol. 57, no. 5, pp. 052202-052202.
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Hsieh, M. 2015, 'Classical Analog to Entanglement Reversibility', Physical Review Letters, vol. 115, no. 9, pp. 1-5.
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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
Brun, T.A., Hsieh, M.H. & Perry, C. 2015, 'Compatibility of state assignments and pooling of information', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 92, no. 1.
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© 2015 American Physical Society. We say that two (or more) state assignments for one and the same quantum system are compatible if they could represent the assignments of observers with differing information about the system. A criterion for compatibility was proposed in [Phys. Rev. A 65, 032315 (2002)PLRAAN1050-294710.1103/PhysRevA.65.032315]; however, this leaves unanswered the question of whether there are degrees of compatibility which could be represented by some quantitative measure, and whether there is a straightforward procedure whereby the observers can pool their information to arrive at a unique joint state assignment. We argue that such measures are only sensible given some assumption about what kind of information was used in making the state assignments in the first place, and that in general state assignments do not represent all of the information possessed by the observers. However, we examine one particular measure and show that it has a straightforward interpretation, assuming that the information was acquired from a particular type of measurement, and that in this case there is a natural rule for pooling information. We extend this measure to compatibility of states for k observers and show that the value is the solution to a semidefinite program. Similar compatibility measures can be defined for alternative notions of state compatibility, including post-Peierls and equal support compatibilities.
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.
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Wilde, M.M., Hsieh, M. & Babar, Z. 2014, 'Entanglement-Assisted Quantum Turbo Codes', IEEE Transactions On Information Theory, vol. 60, no. 2, pp. 1203-1222.
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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.A., 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.
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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, S.T. & Lee, R.-.K. 2014, 'Local PT symmetry violates the no-signaling principle', Phys. Rev. Lett., vol. 112, no. 13.
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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.
Chitambar, E. & Hsieh, M.H. 2014, 'Asymptotic state discrimination and a strict hierarchy in distinguishability norms', Journal of Mathematical Physics, vol. 55, no. 11.
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© 2014 AIP Publishing LLC. In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state discrimination, and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic LOCC. We use this new criterion to prove a gap in the LOCC and separable distinguishability norms. We then turn to the operational advantage of using two-way classical communication over one-way communication in LOCC processing. With a simple two-qubit product state ensemble, we demonstrate a strict majorization of the two-way LOCC norm over the one-way norm.
Brun, T.A., Devetak, I. & Hsieh, M.-.H. 2014, 'Catalytic Quantum Error Correction', IEEE Transactions on Information Theory, vol. 60, no. 6, pp. 3073-3089.
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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.
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.
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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. 2013, 'One-Shot Entanglement-Assisted Quantum and Classical Communication', IEEE Transactions On Information Theory, vol. 59, no. 3, pp. 1929-1939.
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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. & Winter, A. 2013, 'Quantum-to-classical rate distortion coding', Journal Of Mathematical Physics, vol. 54, no. 4, pp. 1-17.
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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.
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.
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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
Datta, N., Mosonyi, M., Hsieh, M. & Brandão, F.G. 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.
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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.
Chitambar, E. & Hsieh, M.H. 2013, 'Revisiting the optimal detection of quantum information', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 88, no. 2.
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In 1991, Peres and Wootters wrote a seminal paper on the nonlocal processing of quantum information. We return to their classic problem and solve it in various contexts. Specifically, for discriminating the "double trine" ensemble with minimum error, we prove that global operations are more powerful than local operations with classical communication (LOCC). Even stronger, there exists a finite gap between the optimal LOCC probability and that obtainable by separable operations (SEP). Additionally we prove that a two-way, adaptive LOCC strategy can always beat a one-way protocol. Our results demonstrate "nonlocality without entanglement" in two-qubit pure states. © 2013 American Physical Society.
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.
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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, M.M. & Hsieh, M. 2012, 'Public and private resource trade-offs for a quantum channel', Quantum Information Processing, vol. 11, pp. 1465-1501.
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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, M.M. & Hsieh, M. 2012, 'The quantum dynamic capacity formula of a quantum channel', Quantum Information Processing, vol. 11, no. 6, pp. 1431-1463.
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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, M.M. & Hsieh, M.H. 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.
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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.
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We introduce joint difference sets as a generalization of cyclic difference sets, and we construct a new class of quantum error-correcting codes (QECCs) from these joint difference sets. The main benefits of our method are as follows. First, we can construct quantum codes that are both high rate and with large block length, while maintaining good performance. Second, the density of constructed quantum parity check matrix can approach zero when the code length is very large. This allows us to use a simple iterative decoding algorithm. Interestingly, our method yields the well-known [5,1,3] QECC. © 2012 World Scientific Publishing Company.
Hsieh, M. & Le Gall, F. 2011, 'NP-hardness of decoding quantum error-correction codes', Physical Review A, vol. 83, no. 5, pp. 1-5.
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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.
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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. 2011, 'The apex of the family tree of protocols: Optimal rates and resource inequalities', New Journal of Physics, vol. 13.
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We establish bounds on the maximum entanglement gain and minimum quantum communication cost of the fully quantum Slepian-Wolf (FQSW) protocol in the one-shot regime, which is considered to be at the apex of the existing family tree in quantum information theory. These quantities, which are expressed in terms of smooth min- and max-entropies, reduce to the known rates of quantum communication cost and entanglement gain in the asymptotic independent and identically distributed scenario. We also provide an explicit proof of the optimality of these asymptotic rates.We introduce a resource inequality for the one-shot FQSW protocol, which in conjunction with our results yields achievable one-shot rates of its children protocols. In particular, it yields bounds on the one-shot quantum capacity of a noisy channel in terms of a single entropic quantity, unlike previous bounds. We also obtain an explicit expression for the achievable rate for one-shot state redistribution.© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
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.
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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.
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.
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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. & Wilde, M.M. 2010, 'Entanglement-assisted communication of classical and quantum Information', IEEE Transactions On Information Theory, vol. 56, no. 9, pp. 4682-4704.
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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.
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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.
Datta, N. & Hsieh, M.H. 2010, 'Universal coding for transmission of private information', Journal of Mathematical Physics, vol. 51, no. 12.
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We consider the scenario in which Alice transmits private classical messages to Bob via a classical-quantum channel, part of whose output is intercepted by an eavesdropper Eve. We prove the existence of a universal coding scheme under which Alice's messages can be inferred correctly by Bob, and yet Eve learns nothing about them. The code is universal in the sense that it does not depend on specific knowledge of the channel. Prior knowledge of the probability distribution on the input alphabet of the channel, and bounds on the corresponding Holevo quantities of the output ensembles at Bob,s and Eve's end suffice. © 2010 American Institute of Physics.
Hsieh, M.H., Brun, T.A. & Devetak, I. 2009, 'Entanglement-assisted quantum quasicyclic low-density parity-check codes', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 79, no. 3.
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We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasicyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Skor-Steane construction do not need to satisfy the dual-containing property as long as preshared entanglement is available to both sender and receiver. We can use this to avoid the many four cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement. © 2009 The American Physical Society.
Hsieh, M.H. & Wilde, M.M. 2009, 'Public and private communication with a quantum channel and a secret key', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 80, no. 2.
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We consider using a secret key and a noisy quantum channel to generate noiseless public communication and noiseless private communication. The optimal protocol for this setting is the publicly enhanced private father protocol. This protocol exploits random coding techniques and "piggybacking" of public information along with secret-key-assisted private codes. The publicly enhanced private father protocol is a generalization of the secret-key-assisted protocol of Hsieh, Luo, and Brun and a generalization of a protocol for simultaneous communication of public and private information suggested by Devetak and Shor. © 2009 The American Physical Society.
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.
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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, T.A. 2008, 'Classical enhancement of quantum-error-correcting codes', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 78, no. 1.
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© 2008 The American Physical Society. We present a general formalism for quantum-error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted coding theory and the classical coding theory in the sense that, after the encoding, error-correcting, and decoding steps, the encoded quantum and classical information can be correctly recovered by the receiver. We formally define this kind of quantum codes using stabilizer language, and derive the appropriate error-correcting conditions. We give several examples to demonstrate the construction of such codes.
Hsieh, M.H., Devetak, I. & Brun, T. 2007, 'General entanglement-assisted quantum error-correcting codes', Physical Review A - Atomic, Molecular, and Optical Physics, vol. 76, no. 6.
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Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting 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 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. © 2007 The American Physical Society.
Brun, T., Devetak, I. & Hsieh, M. 2006, 'Correcting Quantum Errors with Entanglement', Science, vol. 314, no. 5798, pp. 436-439.
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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.
Cheng, H.-.C. & Hsieh, M.-.H., 'Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing'.
In this work, 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 slower than $1/\sqrt{n}$, 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. & Hsieh, M.-.H., 'Round Complexity in the Local Transformations of Quantum and Classical States'.
A natural operational paradigm for distributed quantum and classical information processing involves local operations coordinated by multiple rounds of public communication. In this paper we consider the minimum number of communication rounds needed to perform the locality-constrained task of entanglement transformation and the analogous classical task of secrecy manipulation. Specifically we address whether bipartite mixed entanglement can always be converted into pure entanglement or whether unsecure classical correlations can always be transformed into secret shared randomness using local operations and a bounded number of communication exchanges. Our main contribution in this paper is an explicit construction of quantum and classical state transformations which, for any given $r$, can be achieved using $r$ rounds of classical communication exchanges but no fewer. 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. The major technical contribution of this manuscript lies in proving lower bounds for the required number of communication exchanges using the notion of common information and various lemmas built upon it. We propose a classical analog to the Schmidt rank of a bipartite quantum state which we call the secrecy rank, and we show that it is a monotone under stochastic local classical operations.
Cheng, H.-.C. & Hsieh, M.-.H., 'New Characterizations of Matrix $$-Entropies, Poincaré and Sobolev Inequalities and an Upper Bound to Holevo Quantity'.
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., 'The Learnability of Unknown Quantum Measurements', QIC, vol. 16, pp. 7-8.
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, K.Y., Hsieh, M.-.H. & Koshiba, T., 'A Weak Quantum Oblivious Transfer'.
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., 'Entanglement-assisted Coding Theory'.
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.
Anshu, A., Hsieh, M.-.H. & Jain, R., 'Quantifying resource in catalytic resource theory'.
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.

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Cheng, H.-.C., Hsieh, M.-.H. & Tomamichel, M., 'Sphere-Packing Bound for Symmetric Classical-Quantum Channels'.
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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. The established pre-factor is essentially 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.
Cheng, H.-.C., Hsieh, M.-.H. & Tomamichel, M., 'Quantum Sphere-Packing Bounds with Polynomial Prefactors'.
We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for classical-quantum channels; however, the exponents in their bounds only coincide when the channel is classical. In this paper, we show that these two exponents admit a variational representation and are related by the Golden-Thompson inequality, reaffirming that Dalai's expression is stronger in general classical-quantum channels. Second, we establish a sphere-packing bound for classical-quantum channels, which significantly improves Dalai's 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. Finally, for a special class of symmetric classical-quantum channels, we can completely characterize its optimal error probability without the constant composition code assumption. The main technical contributions are two converse Hoeffding bounds for quantum hypothesis testing and the saddle-point properties of error exponent functions.