#### Can supervise: YES

#### Publications

Chen, J., Guo, C., Ji, Z., Poon, Y.T., Yu, N., Zeng, B. & Zhou, J. 2017, 'Joint product numerical range and geometry of reduced density matrices', *Science China: Physics, Mechanics and Astronomy*, vol. 60, no. 2.View/Download from: Publisher's site

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© 2016, Science China Press and Springer-Verlag Berlin Heidelberg. The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of . We show that, a ruled surface on sitting in has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of , with two boundary pieces of symmetry breaking origin separated by two gapless lines.

Chen, J.Y., Ji, Z., Liu, Z.X., Qi, X., Yu, N., Zeng, B. & Zhou, D. 2017, 'Physical origins of ruled surfaces on the reduced density matrices geometry', *Science China: Physics, Mechanics and Astronomy*, vol. 60, no. 2.View/Download from: Publisher's site

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© 2016, Science China Press and Springer-Verlag Berlin Heidelberg. The reduced density matrices (RDMs) of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical origins of these ruled surfaces for bosonic systems. The emergence of ruled surfaces was recently proposed as signatures of symmetry-breaking phase. We show that, apart from being signatures of symmetry-breaking, ruled surfaces can also be the consequence of gapless quantum systems by demonstrating an explicit example in terms of a two-mode Ising model. Our analysis was largely simplified by the quantum de Finetti's theorem—in the limit of large system size, these RDMs are the convex set of all the symmetric separable states. To distinguish ruled surfaces originated from gapless systems from those caused by symmetry-breaking, we propose to use the finite size scaling method for the corresponding geometry. This method is then applied to the two-mode XY model, successfully identifying a ruled surface as the consequence of gapless systems.

Haah, J., Harrow, A.W., Ji, Z., Wu, X. & Yu, N. 2017, 'Sample-Optimal Tomography of Quantum States', *IEEE Transactions on Information Theory*, vol. 63, no. 9, pp. 5628-5641.View/Download from: UTS OPUS or Publisher's site

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© 1963-2012 IEEE. It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error \epsilon in trace distance required O(dr^{2}/\epsilon ^{2}) copies for a d -dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O (dr/ \delta) \ln ~(d/\delta) copies to estimate \rho to error \delta in infidelity, and a matching lower bound up to logarithmic factors. This implies O((dr / \epsilon ^{2}) \ln ~(d/\epsilon)) copies suffice to achieve error \epsilon in trace distance. We also prove that for independent (product) measurements, \Omega (dr^{2}/\delta ^{2}) / \ln (1/\delta) copies are necessary in order to achieve error \delta in infidelity. For fixed d , our measurement can be implemented on a quantum computer in time polynomial in n.

Xin, T., Lu, D., Klassen, J., Yu, N., Ji, Z., Chen, J., Ma, X., Long, G., Zeng, B. & Laflamme, R. 2017, 'Quantum State Tomography via Reduced Density Matrices.', *Physical review letters*, vol. 118, no. 2, p. 020401.View/Download from: UTS OPUS or Publisher's site

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Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.

Chen, J., Ji, Z., Yu, N. & Zeng, B. 2016, 'Detecting consistency of overlapping quantum marginals by separability', *Physical Review A*, vol. 93, no. 3.View/Download from: UTS OPUS or Publisher's site

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© 2016 American Physical Society. The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many nontrivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the k-symmetric extension problem in general and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known k-symmetric extension criterion for separability.

Chen, J.Y., Ji, Z., Liu, Z.X., Shen, Y. & Zeng, B. 2016, 'Geometry of reduced density matrices for symmetry-protected topological phases', *Physical Review A*, vol. 93, no. 1.View/Download from: UTS OPUS or Publisher's site

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© 2016 American Physical Society. In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low-dimensional projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system - no ruled surface emerges in systems without a boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit where the ground-state degeneracy is exact, we analyze the precision of our numerical algorithm and show that a finite-system calculation suffices to reveal the ruled surface structures.

Chen, J.Y., Ji, Z., Yu, N. & Zeng, B. 2016, 'Entanglement depth for symmetric states', *Physical Review A*, vol. 94, no. 4.View/Download from: Publisher's site

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© 2016 American Physical Society. Entanglement depth characterizes the minimal number of particles in a system that are mutually entangled. For symmetric states, there is a dichotomy for entanglement depth: An N-particle symmetric state is either fully separable or fully entangled - the entanglement depth is either 1 or N. We show that this dichotomy property for entangled symmetric states is even stable under nonsymmetric noise. We propose an experimentally accessible method to detect entanglement depth in atomic ensembles based on a bound on the particle number population of Dicke states, and demonstrate that the entanglement depth of some Dicke states, for example the twin Fock state, is very stable even under a large arbitrary noise. Our observation can be applied to atomic Bose-Einstein condensates to infer that these systems can be highly entangled with the entanglement depth that is on the order of the system size (i.e., several thousands of atoms).

Lu, D., Xin, T., Yu, N., Ji, Z., Chen, J., Long, G., Baugh, J., Peng, X., Zeng, B. & Laflamme, R. 2016, 'Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables.', *Physical review letters*, vol. 116, no. 23, p. 230501.View/Download from: UTS OPUS or Publisher's site

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Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.

Ma, X., Jackson, T., Zhou, H., Chen, J., Lu, D., Mazurek, M.D., Fisher, K.A.G., Peng, X., Kribs, D., Resch, K.J., Ji, Z., Zeng, B. & Laflamme, R. 2016, 'Pure-state tomography with the expectation value of Pauli operators', *Physical Review A*, vol. 93, no. 3.View/Download from: UTS OPUS or Publisher's site

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© 2016 American Physical Society. We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure-state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

Wang, H.Y., Zheng, W.Q., Yu, N.K., Li, K.R., Lu, D.W., Xin, T., Li, C., Ji, Z.F., Kribs, D., Zeng, B., Peng, X.H. & Du, J.F. 2016, 'Quantum state and process tomography via adaptive measurements', *Science China: Physics, Mechanics and Astronomy*, vol. 59, no. 10.View/Download from: Publisher's site

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© 2016, Science China Press and Springer-Verlag Berlin Heidelberg.We investigate quantum state tomography (QST) for pure states and quantum process tomography (QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography (AUPT) protocol of d2+d1 measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate (/8 phase gate), and controlled-NOT gate, respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.

Chen, J., Ji, Z., Li, C.K., Poon, Y.T., Shen, Y., Yu, N., Zeng, B. & Zhou, D. 2015, 'Discontinuity of maximum entropy inference and quantum phase transitions', *New Journal of Physics*, vol. 17, no. 8, pp. 1-19.View/Download from: UTS OPUS or Publisher's site

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© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. In this paper, we discuss the connection between two genuinely quantum phenomena - the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable me asurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.

Chen, J., Ji, Z., Kribs, D., Lütkenhaus, N. & Zeng, B. 2014, 'Symmetric extension of two-qubit states', *Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 90, no. 3, pp. 032318-1-032318-10.View/Download from: UTS OPUS or Publisher's site

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© 2014 American Physical Society. A bipartite state AB is symmetric extendible if there exists a tripartite state ABB whose AB and AB marginal states are both identical to AB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state AB; specifically, tr(B2)tr(AB2)-4detAB. As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.

Chen, J., Dawkins, H., Ji, Z., Johnston, N., Kribs, D., Shultz, F. & Zeng, B. 2013, 'Uniqueness of quantum states compatible with given measurement results', *Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 88, no. 1.View/Download from: UTS OPUS or Publisher's site

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We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states. © 2013 American Physical Society.

Chen, J., Ji, Z., Klyachko, A., Kribs, D.W. & Zeng, B. 2012, 'Rank reduction for the local consistency problem', *Journal of Mathematical Physics*, vol. 53, no. 2.View/Download from: UTS OPUS or Publisher's site

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We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. © 2012 American Institute of Physics.

Chen, J., Ji, Z., Kribs, D., Wei, Z. & Zeng, B. 2012, 'Ground-state spaces of frustration-free Hamiltonians', *Journal of Mathematical Physics*, vol. 53, no. 10.View/Download from: UTS OPUS or Publisher's site

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We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of "reduced spaces" to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set k of all the k-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in k, called atoms, are analogs of extreme points. We study the properties of atoms in k and discuss its relationship with ground states of k-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in 2 are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in k may not be the join of atoms, indicating a richer structure for k beyond the convex structure. Our study of k deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from the new perspective of reduced spaces. © 2012 American Institute of Physics.

Chen, J., Ji, Z., Ruskai, M.B., Zeng, B. & Zhou, D.L. 2012, 'Comment on some results of Erdahl and the convex structure of reduced density matrices', *Journal of Mathematical Physics*, vol. 53, no. 7.View/Download from: Publisher's site

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In [J. Math. Phys.13, 1608-1621 (1972)], Erdahl10.1063/1.1665885 considered the convex structure of the set of N-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the m-body setting and to the more general quantum marginal problem. We describe these extensions, but cannot resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when 2m N every extreme point of the set of N-representable m-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary m-body and (N - m)-body reduced density matrices. © 2012 American Institute of Physics.

Chen, J., Ji, Z., Wei, Z. & Zeng, B. 2012, 'Correlations in excited states of local Hamiltonians', *Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 85, no. 4.View/Download from: UTS OPUS or Publisher's site

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Physical properties of the ground and excited states of a k-local Hamiltonian are largely determined by the k-particle reduced density matrices (k-RDMs), or simply the k-matrix for fermionic systems-they are at least enough for the calculation of the ground-state and excited-state energies. Moreover, for a nondegenerate ground state of a k-local Hamiltonian, even the state itself is completely determined by its k-RDMs, and therefore contains no genuine k-particle correlations, as they can be inferred from k-particle correlation functions. It is natural to ask whether a similar result holds for nondegenerate excited states. In fact, for fermionic systems, it has been conjectured that any nondegenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any nondegenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure n-particle states. We construct explicit counterexamples to show that both conjectures are false. We further show that any nondegenerate excited state of a k-local Hamiltonian is a unique ground state of another 2k-local Hamiltonian, hence is uniquely determined by its 2k-RDMs (or 2k-matrix). These results set up a solid framework for the study of excited-state properties of many-body systems. © 2012 American Physical Society.

Chen, J., Ji, Z., Zeng, B. & Zhou, D.L. 2012, 'From ground states to local Hamiltonians', *Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 86, no. 2.View/Download from: UTS OPUS or Publisher's site

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Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest-neighbor interactions on some types of lattices. A necessary condition for a space V to be the ground-state space of some local Hamiltonian with a given interaction pattern is that the maximally mixed state supported on V is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have V satisfying the necessary condition mentioned above as its ground-state space by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles. © 2012 American Physical Society.

Jain, R., Ji, Z., Upadhyay, S. & Watrous, J. 2011, 'QIP = PSPACE', *Journal of the ACM*, vol. 58, no. 6.View/Download from: UTS OPUS or Publisher's site

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This work considers the quantum interactive proof system model of computation, which is the (classical) interactive proof system model's natural quantum computational analogue. An exact characterization of the expressive power of quantum interactive proof systems is obtained: the collection of computational problems having quantum interactive proof systems consists precisely of those problems solvable by deterministic Turing machines that use at most a polynomial amount of space (or, more succinctly, QIP = PSPACE). This characterization is proved through the use of a parallelized form of the matrix multiplicative weights update method, applied to a class of semidefinite programs that captures the computational power of quantum interactive proof systems. One striking implication of this characterization is that quantum computing provides no increase in computational power whatsoever over classical computing in the context of interactive proof systems, for it is well known that the collection of computational problems having classical interactive proof systems coincides with those problems solvable by polynomial-space computations. © 2011.

Ji, Z., Wei, Z. & Zeng, B. 2011, 'Complete characterization of the ground-space structure of two-body frustration-free Hamiltonians for qubits', *Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 84, no. 4.View/Download from: UTS OPUS or Publisher's site

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The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground-state degeneracy is as hard as, but no harder than, its classical analog. © 2011 American Physical Society.

Ocko, S.A., Chen, X., Zeng, B., Yoshida, B., Ji, Z., Ruskai, M.B. & Chuang, I.L. 2011, 'Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem.', *Physical review letters*, vol. 106, no. 11, p. 110501.View/Download from: UTS OPUS or Publisher's site

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It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

Chen, J., Chen, X., Duan, R., Ji, Z. & Zeng, B. 2011, 'No-go Theorem For One-way Quantum Computing On Naturally Occurring Two-level Systems', *Physical Review A*, vol. 83, no. 5, pp. 0-0.View/Download from: UTS OPUS or Publisher's site

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The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin- 5 2 and spin- 3 2 systems. It is, of course, desirable to have a natural resource state in a spin- 1 2 , that is, qubit system. Here, we give a negative answer to this question for frustration-free systems with two-body interactions. In fact, it is shown to be impossible for any genuinely entangled qubit state to be a nondegenerate ground state of any two-body frustration-free Hamiltonian. What is more, we also prove that every spin- 1 2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states. In other words, there cannot be any interesting entanglement features in the ground state of such a qubit Hamiltonian.

Grassl, M., Ji, Z., Wei, Z. & Zeng, B. 2010, 'Quantum-capacity-approaching codes for the detected-jump channel', *Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 82, no. 6.View/Download from: Publisher's site

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The quantum-channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity-approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel. © 2010 The American Physical Society.

Ji, Z., Chen, J., Wei, Z. & Ying, M. 2010, 'The LU-LC conjecture is false', *Quantum Information and Computation*, vol. 10, no. 1, pp. 97-108.View/Download from: UTS OPUS

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The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false.

Chen, L., Chitambar, E., Duan, R., Ji, Z. & Winter, A. 2010, 'Tensor rank and stochastic entanglement catalysis for multipartite pure states.', *Physical review letters*, vol. 105, no. 20, p. 200501.View/Download from: Publisher's site

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The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state |W3>=1/3(|100> + |010> + |001>) and its N-partite generalization |W(N)>. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of |W3> have a rank of either 15 or 16, (ii) two copies of |W(N)> have a rank of 3N - 2, and (iii) n copies of |W(N)> have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states.

Chen, L., Chitambar, E.A., Duan, R., Ji, Z. & Winter, A. 2010, 'Tensor Rank And Stochastic Entanglement Catalysis For Multipartite Pure States', *Physical Review Letters*, vol. 105, no. 20, pp. 1-4.View/Download from: UTS OPUS or Publisher's site

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The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investig

Chen, X., Duan, R., Ji, Z. & Zeng, B. 2010, 'Quantum State Reduction For Universal Measurement Based Computation', *Physical Review Letters*, vol. 105, no. 2, pp. 1-4.View/Download from: UTS OPUS or Publisher's site

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Measurement based quantum computation, which requires only single particle measurements on a universal resource state to achieve the full power of quantum computing, has been recognized as one of the most promising models for the physical realization of

Ying, M., Feng, Y., Duan, R. & Ji, Z. 2009, 'An Algebra Of Quantum Processes', *Acm Transactions On Computational Logic*, vol. 10, no. 3, pp. 1-36.View/Download from: UTS OPUS or Publisher's site

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We introduce an algebra qCCS of pure quantum processes in which communications by moving quantum states physically are allowed and computations are modeled by super-operators, but no classical data is explicitly involved. An operational semantics of qCCS is presented in terms of (nonprobabilistic) labeled transition systems. Strong bisimulation between processes modeled in qCCS is defined, and its fundamental algebraic properties are established, including uniqueness of the solutions of recursive equations. To model sequential computation in qCCS, a reduction relation between processes is defined. By combining reduction relation and strong bisimulation we introduce the notion of strong reduction-bisimulation, which is a device for observing interaction of computation and communication in quantum systems. Finally, a notion of strong approximate bisimulation (equivalently, strong bisimulation distance) and its reduction counterpart are introduced. It is proved that both approximate bisimilarity and approximate reduction-bisimilarity are preserved by various constructors of quantum processes. This provides us with a formal tool for observing robustness of quantum processes against inaccuracy in the implementation of its elementary gates.

Chen, J.F., Duan, R., Ji, Z., Ying, M. & Yu, J.X. 2008, 'Existence Of Universal Entangler', *Journal of Mathematical Physics*, vol. 49, no. 1, pp. 1-7.View/Download from: UTS OPUS or Publisher's site

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A gate is called an entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for gener

Chitambar, E.A., Duan, R. & Shi, Y. 2008, 'Tripartite Entanglement Transformations And Tensor Rank', *Physical Review Letters*, vol. 101, no. 14, pp. 1-4.View/Download from: UTS OPUS or Publisher's site

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A basic question regarding quantum entangled states is whether one can be probabilistically converted to another through local operations and classical communication exclusively. While the answer for bipartite systems is known, we show that for tripartit

Ji, Z., Wang, G., Duan, R., Feng, Y. & Ying, M. 2008, 'Parameter Estimation of Quantum Channels', *IEEE Transactions On Information Theory*, vol. 54, no. 11, pp. 5172-5185.View/Download from: UTS OPUS or Publisher's site

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The efficiency of parameter estimation of quantum channels is studied in this paper. We introduce the concept of programmable parameters to the theory of estimation. It is found that programmable parameters obey the standard quantum limit strictly; hence, no speedup is possible in its estimation. We also construct a class of nonunitary quantum channels whose parameter can be estimated in a way that the standard quantum limit is broken. The study of estimation of general quantum channels also enables an investigation of the effect of noises on quantum estimation.

Duan, R., Feng, Y., Ji, Z. & Ying, M. 2007, 'Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations And Classical Communication', *Physical Review Letters*, vol. 98, no. 23, pp. 1-4.View/Download from: UTS OPUS

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We show that an arbitrary basis of a multipartite quantum state space consisting of K distant parties such that the kth party has local dimension d(k) always contains at least N=Sigma(K)(k=1)(d(k)-1)+1 members that are unambiguously distinguishable using

Duan, R., Feng, Y., Ji, Z. & Ying, M. 2007, 'Distinguishing arbitrary multipartite basis unambiguously using local operations and classical communication (vol 98, art no 230602, 2007)', *PHYSICAL REVIEW LETTERS*, vol. 99, no. 1.View/Download from: Publisher's site

Feng, Y., Duan, R., Ji, Z. & Ying, M. 2007, 'Probabilistic Bisimulations For Quantum Processes', *Information And Computation*, vol. 205, no. 11, pp. 1608-1639.View/Download from: UTS OPUS or Publisher's site

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Modeling and reasoning about concurrent quantum systems is very important for both distributed quantum computing and quantum protocol verification. As a consequence, a general framework formally describing communication and concurrency in complex quantum

Feng, Y., Duan, R., Ji, Z. & Ying, M. 2007, 'Proof Rules For The Correctness Of Quantum Programs', *Theoretical Computer Science*, vol. 386, no. 1-2, pp. 151-166.View/Download from: UTS OPUS or Publisher's site

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We apply the notion of quantum predicate proposed by D'Hondt and Panangaden to analyze a simple language fragment which may describe the quantum part of a future quantum computer in Knill's architecture. The notion of weakest liberal precondition semanti

Wei, Z. & Ying, M. 2006, 'Majorization In Quantum Adiabatic Algorithms', *Physical Review A*, vol. 74, no. 4, pp. 1-7.View/Download from: UTS OPUS

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The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to appear universall

Duan, R., Ji, Z., Feng, Y. & Ying, M. 2006, 'Some Issues In Quantum Information Theory', *Journal Of Computer Science And Technology*, vol. 21, no. 5, pp. 776-789.View/Download from: UTS OPUS or Publisher's site

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Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the pri

Feng, Y., Duan, R. & Ji, Z. 2006, 'Optimal Dense Coding With Arbitrary Pure Entangled States', *Physical Review A*, vol. 74, no. 1, pp. 1-5.View/Download from: UTS OPUS

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We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in unambiguous dense codi

Feng, Y., Duan, R. & Ji, Z. 2006, 'Optimal dense coding with arbitrary pure entangled states', *Physical Review A*, vol. 74, no. 1.View/Download from: Publisher's site

Ji, Z., Feng, Y., Duan, R. & Ying, M. 2006, 'Boundary Effect Of Deterministic Dense Coding', *Physical Review A*, vol. 73, no. 3, pp. 1-3.View/Download from: UTS OPUS

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We present a rigorous proof of an interesting boundary effect of deterministic dense coding first observed by S. Mozes, J. Oppenheim, and B. Reznik [Phys. Rev. A 71, 012311 (2005)]. Namely, it is shown that d(2)-1 cannot be the maximal alphabet size of a

Ji, Z., Feng, Y., Duan, R. & Ying, M. 2006, 'Identification And Distance Measures Of Measurement Apparatus', *Physical Review Letters*, vol. 96, no. 20, pp. 1-4.View/Download from: UTS OPUS

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We propose simple schemes that can perfectly identify projective measurement apparatuses secretly chosen from a finite set. Entanglement is used in these schemes both to make possible the perfect identification and to improve the efficiency significantly

Ji, Z., Cao, H. & Ying, M. 2005, 'Optimal Conclusive Discrimination Of Two States Can Be Achieved Locally', *Physical Review A*, vol. 71, no. 3, pp. 1-5.View/Download from: UTS OPUS

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This paper constructs a local operation and classical communication protocol that achieves the global optimality of conclusive discrimination of any two pure states with arbitrary a priori probability. This can be interpreted that there is no

Ji, Z., Feng, Y. & Ying, M. 2005, 'Local Cloning Of Two Product States', *Physical Review A*, vol. 72, no. 3, pp. 1-5.View/Download from: UTS OPUS

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Local quantum operations and classical communication (LOCC) put considerable constraints on many quantum information processing tasks such as cloning and discrimination. Surprisingly, however, discrimination of any two pure states survives such constrain

Duan, R., Feng, Y., Ji, Z. & Ying, M. 2005, 'Efficiency Of Deterministic Entanglement Transformation', *Physical Review A*, vol. 71, no. 2, pp. 1-7.View/Download from: UTS OPUS

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We prove that sufficiently many copies of a bipartite entangled pure state can always be transformed into some copies of another one with certainty by local quantum operations and classical communication. The efficiency of such a transformation is charac

Feng, Y., Duan, R. & Ji, Z. 2005, 'Condition And Capability Of Quantum State Separation', *Physical Review A*, vol. 72, no. 1, pp. 1-6.View/Download from: UTS OPUS

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The linearity of quantum operations puts many fundamental constraints on the information processing tasks we can achieve on a quantum system whose state is not exactly known, just as we observe in quantum cloning and quantum discrimination. In this paper

Feng, Y., Duan, R. & Ji, Z. 2005, 'Condition and capability of quantum state separation', *Physical Review A*, vol. 72, no. 1.View/Download from: Publisher's site

Duan, R., Ji, Z., Feng, Y. & Ying, M. 2004, 'Quantum Operation Quantum Fourier Transform And Semi-Definite Programming', *Physics Letters A*, vol. 323, no. 1-2, pp. 48-56.View/Download from: UTS OPUS or Publisher's site

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We analyze a class of quantum operations based on a geometrical representation of d-level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for

Ji, Z., Duan, R. & Ying, M. 2004, 'Comparability Of Multipartite Entanglement', *Physics Letters A*, vol. 330, no. 6, pp. 418-423.View/Download from: UTS OPUS or Publisher's site

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We prove, in a multipartite setting, that it is always feasible to exactly transform a genuinely m-partite entangled pure state with sufficient many copies to any other m-partite state via local quantum operation and classical communication. This result

Ying, M., Duan, R., Feng, Y. & Ji, Z. 2010, 'Predicate Transformer Semantics of Quantum Programs' in Gay, S. & Mackie, I. (eds), *Semantic Techniques in Quantum Computation*, Cambridge University Press, Cambridge, pp. 311-360.View/Download from: UTS OPUS

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This chapter presents a systematic exposition of predicate transformer semantics for quantum programs. It is divided into two parts: The first part reviews the state transformer (forward) semantics of quantum programs according to Selingerâs suggestion of representing quantum programs by superoperators and elucidates DâHondt-Panangadenâs theory of quantum weakest preconditions in detail. In the second part, we develop a quite complete predicate transformer semantics of quantum programs based on Birkhoffâvon Neumann quantum logic by considering only quantum predicates expressed by projection operators. In particular, the universal coujunctivity and termination law of quantum programs are proved, and Hoareâs induction rule is established in the quantum setting.

Ji, Z. 2017, 'Compression of quantum multi-prover interactive proofs', *Proceedings of the Annual ACM Symposium on Theory of Computing*, ACM SIGACT Symposium on Theory of Computing, AM, Montreal, Canada, pp. 289-302.View/Download from: Publisher's site

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© 2017 ACM. We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, it follows that the promise problem corresponding to the approximation of the nonlocal value to inverse polynomial accuracy is complete for QMIP, and therefore NEXP-hard. This establishes that nonlocal games are provably harder than classical games without any complexity theory assumptions. Our result also indicates that gap amplification for nonlocal games may be impossible in general and provides a negative evidence for the feasibility of the gap amplification approach to the multi-prover variant of the quantum PCP conjecture.

Cui, S.X., Ji, Z., Yu, N. & Zeng, B. 2016, 'Quantum Capacities for Entanglement Networks', *Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT)*, IEEE International Symposium on Information Theory, IEEE, Barcelona, Spain, pp. 1685-1689.View/Download from: UTS OPUS or Publisher's site

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We discuss quantum capacities for two types of entanglement networks: Q for the quantum repeater network with free classical communication, and R for the tensor network as the rank of the linear operation represented by the tensor network. We find that Q always equals R in the regularized case for the same network graph. However, the relationships between the corresponding one-shot capacities Q1 and R1 are more complicated, and the min-cut upper bound is in general not achievable. We show that the tensor network can be viewed as a stochastic protocol with the quantum repeater network, such that R1 is a natural upper bound of Q1. We analyze the possible gap between R1 and Q1 for certain networks, and compare them with the one-shot classical capacity of the corresponding classical network.

Haah, J., Harrow, A.W., Ji, Z., Wu, X. & Yu, N. 2016, 'Sample-optimal tomography of quantum states', *STOC '16 Proceedings of the forty-eighth annual ACM symposium on Theory of Computing*, ACM symposium on Theory of Computing, ACM, Cambridge, MA, USA, pp. 913-925.View/Download from: UTS OPUS or Publisher's site

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It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. This is the quantum analogue of the problem of estimating a probability distribution given some number of samples.

Previously, it was known only that estimating states to error in trace distance required O(dr2/2) copies for a d-dimensional density matrix of rank r. Here, we give a measurement scheme (POVM) that uses O( (dr/ ) ln(d/) ) copies to estimate to error in infidelity. This implies O( (dr / 2) ln(d/) ) copies suffice to achieve error in trace distance. For fixed d, our measurement can be implemented on a quantum computer in time polynomial in n.

We also use the Holevo bound from quantum information theory to prove a lower bound of (dr/2)/ log(d/r) copies needed to achieve error in trace distance. This implies a lower bound (dr/)/log(d/r) for the estimation error in infidelity. These match our upper bounds up to log factors.

Our techniques can also show an (r2d/) lower bound for measurement strategies in which each copy is measured individually and then the outcomes are classically post-processed to produce an estimate. This matches the known achievability results and proves for the first time that such 'product measurements have asymptotically suboptimal scaling with d and r.

Ji, Z. 2016, 'Classical verification of quantum proofs', *STOC '16 Proceedings of the forty-eighth annual ACM symposium on Theory of Computing*, ACM symposium on Theory of Computing, ACM, Cambridge, MA, USA, pp. 885-898.View/Download from: Publisher's site

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We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to inverse polynomial precision is QMA-hard. Our work makes an interesting connection between the theory of QMA-completeness and Hamiltonian complexity on one hand and the study of non-local games and Bell inequalities on the other.

Duan, R., Grassl, M., Ji, Z. & Zeng, B. 2010, 'Multi-error-correcting amplitude damping codes', *IEEE International Symposium on Information Theory - Proceedings*, International Symposium on Information Theory, IEEE, Austin, USA, pp. 2672-2676.View/Download from: UTS OPUS or Publisher's site

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We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This allows us to use co