Professor Runyao Duan

Ying, M., Duan, R., Feng, Y. & Ji, Z. 2010, 'Predicate Transformer Semantics of Quantum Programs' in Simon Gay, Ian Mackie (eds), Semantic Techniques in Quantum Computation, Cambridge University Press, Cambridge, pp. 311-360.
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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 SelingerÔ++s suggestion of representing quantum programs by superoperators and elucidates DÔ++Hondt-PanangadenÔ++s theory of quantum weakest preconditions in detail. In the second part, we develop a quite complete predicate transformer semantics of quantum programs based on BirkhoffÔ++von 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 HoareÔ++s induction rule is established in the quantum setting.

Feng, Y., Duan, R. & Ying, M. 2012, 'Bisimulation For Quantum Processes', ACM Transactions pn Programming Language and Systems (TOPLAS), vol. 34, no. 4, pp. 1-43.
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Quantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the oth

Ying, M., Feng, Y., Duan, R., Li, Y. & Yu, N. 2012, 'Quantum Programming: From Theories To Implementations', Chinese Science Bulletin, vol. 57, no. 16, pp. 1903-1909.
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This paper surveys the new field of programming methodology and techniques for future quantum computers, including design of sequential and concurrent quantum programming languages, their semantics and implementations. Several verification methods for qu

Yu, N., Duan, R. & Ying, M. 2012, 'Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States', Physical Review Letters, vol. 109, no. 2, pp. 020506-1-020506-5.
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We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of d locally indistinguishable d?d orthogonal maximally entangled states for some positive integer d. We further show that a 2?2 maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of entanglement discrimination catalysis. Based on this set of states, we construct a new set K consisting of four locally indistinguishable states such that K?m (with 4m members) is locally distinguishable for some m greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.

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.
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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.

Yu, N., Duan, R. & Ying, M. 2011, 'Any 2 Circle Times N Subspace Is Locally Distinguishable', Physical Review A, vol. 84, no. 1, pp. 1-3.
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A subspace of a multipartite Hilbert space is said to be locally indistinguishable if any orthonormal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that any m . n bipartite system with m > 2 and n > 2 has a locally indistinguishable subspace. However, it has been an open problem since 2005 whether there is a locally indistinguishable bipartite subspace with a qubit subsystem.We settle this problem in negative by showing that any 2 . n bipartite subspace contains a basis that is locally distinguishable. As an interesting application, we show that any quantum channel with two Kraus operators has optimal environment-assisted classical capacity.

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.
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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.
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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

Chitambar, E.A., Duan, R. & Shi, Y. 2010, 'Multipartite-To-Bipartite Entanglement Transformations And Polynomial Identity Testing', Physical Review A, vol. 81, no. 5, pp. 1-4.
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We consider the problem of deciding if some multiparty entangled pure state can be converted, with a nonzero success probability, into a given bipartite pure state shared between two specified parties through local quantum operations and classical commun

Duan, R., Xin, Y. & Ying, M. 2010, 'Locally Indistinguishable Subspaces Spanned By Three-Qubit Unextendible Product Bases', Physical Review A, vol. 81, no. 3, pp. 1-10.
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We study the local distinguishability of general multiqubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that

Duan, R. & Shi, Y. 2010, 'When Is There A Multipartite Maximum Entangled State?', Quantum Information and Computation, vol. 10, no. 11-12, pp. 925-935.
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For a multipartite quantum system of the dimension d(1) circle times d(2) circle times ... circle times d(n), where d(1) >= d(2) >= ... >= d(n) >= 2, is there an entangled state maximum in the sense that all other states in the system can be obtained from the state through local quantum operations and classical communications (LOCC)? When d(1) >= n i=2d(i), such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.

Li, Y., Duan, R. & Ying, M. 2010, 'Local Unambiguous Discrimination With Remaining Entanglement', Physical Review A, vol. 82, no. 3, pp. 1-6.
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A bipartite state, which is secretly chosen from a finite set of known entangled pure states, cannot immediately be useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown state, we i

Yu, N., Chitambar, E.A., Guo, C. & Duan, R. 2010, 'Tensor Rank Of The Tripartite State Vertical Bar W >(Circle Times N)', Physical Review A, vol. 81, no. 1, pp. 1-3.
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Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its nonadditivity as an entanglement measure has recently been observed. In this Brief Report, we estimate the tensor rank of multiple copies of the

Yu, N., Duan, R. & Ying, M. 2010, 'Optimal Simulation Of A Perfect Entangler', Physical Review A, vol. 81, no. 3, pp. 1-4.
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A2 circle times 2 unitary operation is called a perfect entangler if it can generate a maximally entangled state from some unentangled input. We study the following question: How many runs of a given two-qubit entangling unitary operation are required to

Chitambar, E.A. & Duan, R. 2009, 'Nonlocal Entanglement Transformations Achievable by Separable Operations', Physical Review Letters, vol. 103, no. 11, pp. 1-4.
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The weird phenomenon of "quantum nonlocality without entanglement" means that local quantum operations assisted by classical communication constitute a proper subset of the class of separable quantum operations. Despite considerable recent advances, little is known to what extent the class of separable operations differs from local quantum operations and classical communication. In this Letter we show that separable operations are generally stronger than local quantum operations and classical communication when distilling a mixed state into a pure entangled state and thus confirm the existence of entanglement monotones that can increase under separable operations. Our finding can also be interpreted as confirming the ability of separable operations to enhance the entanglement of mixed states relative to certain measures, a sensible but important fact that has never been rigorously proven before.

Duan, R., Feng, Y., Xin, Y. & Ying, M. 2009, 'Distinguishability of Quantum States by Separable Operations', IEEE Transactions On Information Theory, vol. 55, no. 3, pp. 1320-1330.
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In this paper, we study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of (D - 1) pure states, where D is the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of 2 circle times 2 separable operations not being realizable by local operations and classical communication. Before our work, only a class of 3 circle times 3 nonlocal separable operations was known [Bennett et al, Phys. Rev. A 59, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states, i.e., has an orthogonal Schmidt number not less than three, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. 95, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp., three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.

Duan, R., Feng, Y. & Ying, M. 2009, 'Perfect Distinguishability of Quantum Operations', Physical Review Letters, vol. 103, no. 21, pp. 210501-1-210501-4.
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We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretly selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, we find that an optimal perfect discrimination between two isometries is always achievable without auxiliary systems or entanglement.

Feng, Y., Duan, R. & Ying, M. 2009, 'Locally undetermined states, generalized Schmidt decomposition, and application in distributed computing', Quantum Information and Computation, vol. 9, no. 11, pp. 997-1012.
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Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computation. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable and they are not allowed to use local ancillary quantum systems, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state

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.
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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.
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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.
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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

Duan, R. & Shi, Y. 2008, 'Entanglement Between Two Uses Of A Noisy Multipartite Quantum Channel Enables Perfect Transmission Of Classical Information', Physical Review Letters, vol. 101, no. 2, pp. 1-4.
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Suppose that m senders want to transmit classical information to n receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and t

Duan, R., Feng, Y. & Ying, M. 2008, 'Local Distinguishability Of Multipartite Unitary Operations', Physical Review Letters, vol. 100, no. 2, pp. 1-4.
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We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguished by local operations and classical communication when a finite number of runs is allowed. Intuitively, this result indicate

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.
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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.

Wu, X. & Duan, R. 2008, 'Exact Quantum Search By Parallel Unitary Discrimination Schemes', Physical Review A, vol. 78, no. 1, pp. 1-8.
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We study the unsorted database search problem with items N from the viewpoint of unitary discrimination. Instead of considering the famous O(root N) Grover bounded-error algorithm for the original problem, we seek the results for the exact algorithms, i.

Xin, Y. & Duan, R. 2008, 'Local Distinguishability Of Orthogonal 2 Circle Times 3 Pure States', Physical Review A, vol. 77, no. 1, pp. 1-10.
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We present a complete characterization for the local distinguishability of orthogonal 2 circle times 3 pure states except for some special cases of three states. Interestingly, we find there is a large class of four or three states that are indistinguish

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.
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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. & Ying, M. 2007, 'Entanglement Is Not Necessary For Perfect Discrimination Between Unitary Operations', Physical Review Letters, vol. 98, no. 10, pp. 1-4.
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We show that a unitary operation (quantum circuit) secretly chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or joint quantum ope

Feng, Y., Duan, R., Ji, Z. & Ying, M. 2007, 'Probabilistic Bisimulations For Quantum Processes', Information And Computation, vol. 205, no. 11, pp. 1608-1639.
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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.
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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

Xin, Y. & Duan, R. 2007, 'Conditions For Entanglement Transformation Between A Class Of Multipartite Pure States With Generalized Schmidt Decompositions', Physical Review A, vol. 76, no. 4, pp. 1-3.
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We generalize Nielsen's majorization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett. 83, 436 (1999)] to a special class of multipartite pure states with generalized Schmidt decompositions.

Ying, M., Chen, J.F., Feng, Y. & Duan, R. 2007, 'Commutativity Of Quantum Weakest Preconditions', Information Processing Letters, vol. 104, no. 4, pp. 152-158.
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The notion of quantum weakest precondition was introduced by D'Hondt and P. Panangaden [E. D'Hondt, P. Panangaden, Quantum weakest preconditions, Mathematical Structures in Computer Science 16 (2006) 429-451], and they presented a representation of weake

Duan, R., Feng, Y. & Ying, M. 2006, 'Partial Recovery Of Quantum Entanglement', IEEE Transactions On Information Theory, vol. 52, no. 7, pp. 3080-3104.
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Suppose Alice and Bob try to transform an entangled state shared between them into another one by local operations and classical communications. Then in general a certain amount of entanglement contained in the initial state will decrease in the process

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.
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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.
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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. & Ying, M. 2006, 'Relation Between Catalyst-Assisted Transformation And Multiple-Copy Transformation For Bipartite Pure States', Physical Review A, vol. 74, no. 4, pp. 1-7.
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We show that in some cases, catalyst-assisted entanglement transformation cannot be implemented by multiple-copy transformation for pure states. This fact, together with the result we obtained in R. Y. Duan, Y. Feng, X. Li, and M. S. Ying, Phys. Rev. A 7

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.
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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.
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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

Duan, R., Feng, Y., Ji, Z. & Ying, M. 2005, 'Efficiency Of Deterministic Entanglement Transformation', Physical Review A, vol. 71, no. 2, pp. 1-7.
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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

Duan, R., Feng, Y. & Ying, M. 2005, 'Entanglement-Assisted Transformation Is Asymptotically Equivalent To Multiple-Copy Transformation', Physical Review A, vol. 72, no. 2, pp. 1-5.
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We show that two ways of manipulating quantum entanglement-namely, entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)] and multiple-copy transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen

Duan, R., Feng, Y., Li, X. & Ying, M. 2005, 'Multiple-Copy Entanglement Transformation And Entanglement Catalysis', Physical Review A, vol. 71, no. 4, pp. 1-11.
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We prove that any multiple-copy entanglement transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A 65, 052315 (2002)] can be implemented by a suitable entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. R

Duan, R., Feng, Y., Li, X. & Ying, M. 2005, 'Trade-Off Between Multiple-Copy Transformation And Entanglement Catalysis', Physical Review A, vol. 71, no. 6, pp. 1-7.
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We demonstrate that multiple copies of a bipartite entangled pure state may serve as a catalyst for certain entanglement transformations while a single copy cannot. Such a state is termed a

Feng, Y., Duan, R. & Ying, M. 2005, 'Catalyst-Assisted Probabilistic Entanglement Transformation', IEEE Transactions On Information Theory, vol. 51, no. 3, pp. 1090-1101.
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We are concerned with catalyst-assisted probabilistic entanglement transformations. A necessary and sufficient condition is presented under which there exist partial catalysts that can increase the maximal transforming probability of a given entanglement

Feng, Y., Duan, R. & Ji, Z. 2005, 'Condition And Capability Of Quantum State Separation', Physical Review A, vol. 72, no. 1, pp. 1-6.
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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

Sun, X., Duan, R. & Ying, M. 2005, 'The Existence Of Quantum Entanglement Catalysts', IEEE Transactions On Information Theory, vol. 51, no. 1, pp. 75-80.
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Without additional resources, it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication. Jonathan and Plenio (Phys. Rev. Lett., vol. 83, p. 3566, 1999) presented an interesting

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.
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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

Feng, Y., Duan, R. & Ying, M. 2004, 'Unambiguous discrimination between mixed quantum states', Physical Review A, vol. 70, no. 1, pp. 012308-1-012308-4.
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We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if they are orthogonal. The sufficient and necessary condition under which nonorthogonal mixed quantum states can be unambiguously discriminated is also presented. Furthermore, we derive a series of lower bounds on the inconclusive probability of unambiguous discrimination of states from a mixed state set with a priori probabilities.

Feng, Y., Duan, R. & Ying, M. 2004, 'When Catalysis Is Useful For Probabilistic Entanglement Transformation', Physical Review A, vol. 69, no. 6, pp. 1-5.
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We determine all 2x2 quantum states that can serve as useful catalysts for a given probabilistic entanglement transformation, in the sense that they can increase the maximal transformation probability. When higher-dimensional catalysts are considered, a

Ji, Z., Duan, R. & Ying, M. 2004, 'Comparability Of Multipartite Entanglement', Physics Letters A, vol. 330, no. 6, pp. 418-423.
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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

Duan, R., Severini, S. & Winter, A. 2011, 'Zero-error communication via quantum channels and a quantum Lovasz -function', IEEE International Symposium on Information Theory Proceedings (ISIT), St Petersburg, Russia, July 2011 in 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), ed NA, IEEE, Piscataway, USA, pp. 64-68.
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We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain linear space operators as the quantum generalisation of the adjacency matrix, in terms of which the plain, quantum and entanglement-assisted capacity can be formulated, and for which we show some new basic properties. Most importantly, we define a quantum version of Lova¦sz' famous ? function, as the norm-completion (or stabilisation) of a +naive+ generalisation of ?. We go on to show that this function upper bounds the number of entanglement-assisted zero-error messages, that it is given by a semidefinite programme, whose dual we write down explicitly, and that it is multiplicative with respect to the natural (strong) graph product. We explore various other properties of the new quantity, which reduces to Lova¦sz' original ? in the classical case, give several applications, and propose to study the linear spaces of operators associated to channels as +non-commutative graphs+, using the language of operator systems and Hilbert modules.

Feng, Y., Duan, R. & Ying, M. 2011, 'Bisimulation for Quantum Processes', annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages, Austin, Texas, USA, January 2011 in Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language, ed Sagiv, M, ACM, New York, NY, USA, pp. 523-534.
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Quantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the other hand, quantum protocol designers may commit much more faults than classical protocol designers since human intuition is much better adapted to the classical world than the quantum world. To offer formal techniques for modeling and verification of quantum protocols, several quantum extensions of process algebra have been proposed. One of the most serious issues in quantum process algebra is to discover a quantum generalization of the notion of bisimulation, which lies in a central position in process algebra, preserved by parallel composition in the presence of quantum entanglement, which has no counterpart in classical computation. Quite a few versions of bisimulation have been defined for quantum processes in the literature, but in the best case they are only proved to be preserved by parallel composition of purely quantum processes where no classical communications are involved. Many quantum cryptographic protocols, however, employ the LOCC (Local Operations and Classical Communications) scheme, where classical communications must be explicitly specified. So, a notion of bisimulation preserved by parallel composition in the circumstance of both classical and quantum communications is crucial for process algebra approach to verification of quantum cryptographic protocols. In this paper we introduce a novel notion of bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and quantum communications are present.We also establish some basic algebraic laws for this bisimulation.

Duan, R., Grassl, M., Ji, Z., Zeng, B. 2010, 'Multi-error-correcting amplitude damping codes', International Symposium on Information Theory, Austin, USA, June 2010 in IEEE International Symposium on Information Theory - Proceedings, ed NA, IEEE, Piscataway, USA, pp. 2672-2676.
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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