# Professor Runyao Duan

**Future Fellow and Professor,**A/DRsch Ctr Quantum Computat'n & Intelligent Systs

**Core Member,**Centre for Quantum Computation and Intelligent Systems

NA

**Phone**

+61 2 9514 4619

**Room**

CB11.10.206

**Can supervise:**Yes

## Chapters

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. 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 Selingers suggestion of representing quantum programs by superoperators and elucidates DHondt-Panangadens theory of quantum weakest preconditions in detail. In the second part, we develop a quite complete predicate transformer semantics of quantum programs based on Birkhoffvon 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 Hoares induction rule is established in the quantum setting.

## Conferences

Duan, R., Severini, S. & Winter, A. 2011, 'Zero-error communication via quantum channels and a quantum Lovasz -function',

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*2011 IEEE International Symposium on Information Theory Proceedings (ISIT)*, IEEE, Piscataway, USA, pp. 64-68.View/Download from: Publisher's site

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 Lovasz' 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 Lovasz' 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. 2010, 'Bisimulation for quantum processes',

*ACM Transactions on Programming Languages and Systems 2012, vol.34(4), no.17*. In this paper we introduce a novel notion of probabilistic 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. In particular, we prove uniqueness of the
solutions to recursive equations of quantum processes, which provides a
powerful proof technique for verifying complex quantum protocols.

Duan, R., Grassl, M., Ji, Z. & Zeng, B. 2010, 'Multi-Error-Correcting Amplitude Damping Codes',

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*Proceedings 2010 IEEE International Symposium on Information Theory (ISIT 2010), Austin, USA, June 2010, pp. 2672-2676*.View/Download from: Publisher's site

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 concatenated codes with quantum erasure-correcting codes
as outer codes for correcting multiple amplitude damping errors. Our new codes
are degenerate stabilizer codes and have parameters which are better than the
amplitude damping codes obtained by any previously known construction.

## Journal articles

Chitambar, E., Duan, R. & Hsieh, M.H. 2013, 'When do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?',

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*IEEE Trans. Inform. Theory*, vol. 60, p. 3.View/Download from: Publisher's site

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 \emph{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 \textit{almost all}
two-qubit ensembles consisting of three pure states cannot be optimally
discriminated using LOCC. This is surprising considering that \textit{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 $N\to\infty$, 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.

Lu, C., Chen, J. & Duan, R. 2012, 'Some bounds on the minimum number of queries required for quantum channel perfect discrimination',

*Quantum Information and Computation*, vol. 12, no. 1-2, pp. 138-148. We prove a lower bound on the q-maximal fidelities between two quantum channels ? 0 and ? 1 and an upper bound on the q-maximal fidelities between a quantum channel ? and an identity I. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguish ability between ? and I and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating ? and I. Interestingly, in the 2-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in [20], we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating ? and I over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels ? 0 and ? 1 in sequential scheme and over all possible discrimination schemes respectively. Rinton Press.

Ying, M., Feng, Y., Duan, R., Li, Y. & Yu, N. 2012, 'Quantum Programming: From Theories To Implementations',

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*Chinese Science Bulletin*, vol. 57, no. 16, pp. 1903-1909.View/Download from: Publisher's site

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

Feng, Y., Duan, R. & Ying, M. 2012, 'Bisimulation For Quantum Processes',

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*ACM Transactions pn Programming Language and Systems (TOPLAS)*, vol. 34, no. 4, pp. 1-43.View/Download from: Publisher's site

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

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',

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*Physical Review A*, vol. 83, no. 5, pp. 0-0.View/Download from: Publisher's site

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.

This paper develops verification methodology for quantum programs, and the
contribution of the paper is two-fold: 1. Sharir, Pnueli and Hart [SIAM J.
Comput. 13(1984)292-314] presented a general method for proving properties of
probabilistic programs, in which a probabilistic program is modeled by a Markov
chain and an assertion on the output distribution is extended into an invariant
assertion on all intermediate distributions. Their method is essentially a
probabilistic generalization of the classical Floyd inductive assertion method.
In this paper, we consider quantum programs modeled by quantum Markov chains
which are defined by super-operators. It is shown that the Sharir-Pnueli-Hart
method can be elegantly generalized to quantum programs by exploiting the
Schr\"odinger-Heisenberg duality between quantum states and observables. In
particular, a completeness theorem for the Sharir-Pnueli-Hart verification
method of quantum programs is established. 2. As indicated by the completeness
theorem, the Sharir-Pnueli-Hart method is in principle effective for verifying
all properties of quantum programs that can be expressed in terms of Hermitian
operators (observables). But it is not feasible for many practical applications
because of the complicated calculation involved in the verification. For the
case of finite-dimensional state spaces, we find a method for verification of
quantum programs much simpler than the Sharir-Pnueli-Hart method by employing
the matrix representation of super-operators and Jordan decomposition of
matrices. In particular, this method enables us to compute easily the average
running time and even to analyze some interesting long-run behaviors of quantum
programs in a finite-dimensional state space.

Chen, X., Duan, R., Ji, Z. & Zeng, B. 2010, 'Quantum state reduction for universal measurement based computation.',

*Phys Rev Lett*, vol. 105, no. 2, p. 020502. 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 quantum computers. Despite considerable progress in the past decade, it remains a great challenge to search for new universal resource states with naturally occurring Hamiltonians and to better understand the entanglement structure of these kinds of states. Here we show that most of the resource states currently known can be reduced to the cluster state, the first known universal resource state, via adaptive local measurements at a constant cost. This new quantum state reduction scheme provides simpler proofs of universality of resource states and opens up plenty of space to the search of new resource states.

Yu, N., Duan, R. & Ying, M. 2010, 'Optimal Simulation Of A Perfect Entangler',

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*Physical Review A*, vol. 81, no. 3, pp. 1-4.View/Download from: Publisher's site

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

Yu, N., Chitambar, E., Guo, C. & Duan, R. 2010, 'Tensor rank of the tripartite state vertical bar W >(circle times n)',

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*PHYSICAL REVIEW A*, vol. 81, no. 1.View/Download from: Publisher's site

Chen, L., Chitambar, E.A., Duan, R., Ji, Z. & Winter, A. 2010, 'Tensor Rank And Stochastic Entanglement Catalysis For Multipartite Pure States',

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*Physical Review Letters*, vol. 105, no. 20, pp. 1-4.View/Download from: Publisher's site

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

Chitambar, E.A., Duan, R. & Shi, Y. 2010, 'Multipartite-To-Bipartite Entanglement Transformations And Polynomial Identity Testing',

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*Physical Review A*, vol. 81, no. 5, pp. 1-4.View/Download from: Publisher's site

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

Yu, N., Duan, R. & Ying, M. 2010, 'Any $2\otimes n$ subspace is locally distinguishable',

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*Phys. Rev. A*, vol. 84, p. 012304.View/Download from: Publisher's site

A subspace of a multipartite Hilbert space is called \textit{locally
indistinguishable} if any orthogonal basis of this subspace cannot be perfectly
distinguished by local operations and classical communication. Previously it
was shown that any $m\otimes n$ bipartite system such that $m>2$ 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 by showing that any $2\otimes n$
bipartite subspace is locally distinguishable in the sense it contains a basis
perfectly distinguishable by LOCC. As an interesting application, we show that
any quantum channel with two Kraus operations has optimal environment-assisted
classical capacity.

Duan, R., Severini, S. & Winter, A. 2010, 'Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function',

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*IEEE Trans. Inf. Theory 59(2):1164-1174, 2013*.View/Download from: Publisher's site

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 operator space 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 Lovasz' famous theta
function, as the norm-completion (or stabilisation) of a "naive" generalisation
of theta. 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
Lovasz' original theta in the classical case, give several applications, and
propose to study the operator spaces associated to channels as "non-commutative
graphs", using the language of Hilbert modules.

Ying, M., Feng, Y., Duan, R. & Ji, Z. 2009, 'An algebra of quantum processes',

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*ACM Transactions on Computational Logic*, vol. 10, no. 3.View/Download from: Publisher's site

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. 2009 ACM.

Chitambar, E.A. & Duan, R. 2009, 'Nonlocal Entanglement Transformations Achievable by Separable Operations',

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*Physical Review Letters*, vol. 103, no. 11, pp. 1-4.View/Download from: Publisher's site

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. & Shi, Y. 2009, 'When is there a multipartite maximum entangled state?'.

For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes...
d_n$, $d_1\ge d_2\ge...\ge d_n$, is there an entangled state {\em 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
$d_1\ge\Pi_{i=2}^n d_i$, such state exists. We show that this condition is also
necessary. Our proof, somewhat surprisingly, uses results from algebraic
complexity theory.

A bipartite state which is secretly chosen from a finite set of known
entangled pure states cannot be immediately useful in standard quantum
information processing tasks. To effectively make use of the entanglement
contained in this unknown state, we introduce a new way to locally manipulate
the original quantum system: either identify the state successfully or distill
some pure entanglement. Remarkably, if many copies are available, we show that
any finite set of entangled pure states, whatever orthogonal or not, can be
locally distinguished in this way, which further implies that pure entanglement
can be deterministically extracted from unknown pure entanglement. These
results make it clear why a large class of entangled bipartite quantum
operations including unitary operations and measurements that are globally
distinguishable can also be locally distinguishable: they can generate pure
entanglement consistently.

Duan, R. & Shi, Y. 2008, 'Entanglement between two uses of a noisy multipartite quantum channel enables perfect transmission of classical information',

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*PHYSICAL REVIEW LETTERS*, vol. 101, no. 2.View/Download from: Publisher's site

Duan, R., Feng, Y. & Ying, M. 2008, 'Local Distinguishability Of Multipartite Unitary Operations',

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*Physical Review Letters*, vol. 100, no. 2, pp. 1-4.View/Download from: Publisher's site

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

Chitambar, E.A., Duan, R. & Shi, Y. 2008, 'Tripartite Entanglement Transformations And Tensor Rank',

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*Physical Review Letters*, vol. 101, no. 14, pp. 1-4.View/Download from: Publisher's site

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

Feng, Y., Duan, R. & Ying, M. 2008, 'Locally undetermined states, generalized Schmidt decomposition, and an application in distributed computing'.

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.

Xin, Y. & Duan, R. 2008, 'Local distinguishability of orthogonal 2 circle times 3 pure states',

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*PHYSICAL REVIEW A*, vol. 77, no. 1.View/Download from: Publisher's site

Duan, R., Feng, Y., Xin, Y. & Ying, M. 2007, 'Distinguishability of Quantum States by Separable Operations',

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*IEEE Trans. Inform. Theory*, vol. 55, p. 3.View/Download from: Publisher's site

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
$2\otimes 2$ separable operations not being realizable by local operations and
classical communication. Before our work only a class of $3\otimes 3$ nonlocal
separable operations was known [Bennett et al, Phys. Rev. A \textbf{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 1 or 2 orthogonal product
states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize
the recent work about indistinguishable bipartite subspaces [Watrous, Phys.
Rev. Lett. \textbf{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.

Ying, M., Chen, J.F., Feng, Y. & Duan, R. 2007, 'Commutativity Of Quantum Weakest Preconditions',

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*Information Processing Letters*, vol. 104, no. 4, pp. 152-158.View/Download from: Publisher's site

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

Xin, Y. & Duan, R. 2007, 'Conditions for entanglement transformation between a class of multipartite pure states with generalized Schmidt decompositions',

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*PHYSICAL REVIEW A*, vol. 76, no. 4.View/Download from: Publisher's site

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. 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. 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

Chen, J., Duan, R., Ji, Z., Ying, M. & Yu, J. 2007, 'Existence of Universal Entangler'.

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A gate is called 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 generating entanglements, and thus provides important
physical resources for accomplishing many tasks in quantum computing and
quantum information. This Letter demonstrates that a universal entangler always
exists except for a degenerated case. Nevertheless, the problem how to find a
universal entangler remains open.

Feng, Y., Duan, R., Ji, Z. & Ying, M. 2007, 'Probabilistic bisimulations for quantum processes',

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*INFORMATION AND COMPUTATION*, vol. 205, no. 11, pp. 1608-1639.View/Download from: Publisher's site

Feng, Y., Duan, R., Ji, Z. & Ying, M. 2007, 'Proof Rules For The Correctness Of Quantum Programs',

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*Theoretical Computer Science*, vol. 386, no. 1-2, pp. 151-166.View/Download from: Publisher's site

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

Duan, R., Xin, Y. & Ying, M. 2007, 'Locally Indistinguishable Subspaces Spanned by Three-Qubit Unextendible Product Bases'.

We study the local distinguishability of general multi-qubit 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 the local distinguishability of multi-qubit states can be
decided efficiently. Another useful consequence is that a set of orthogonal
$n$-qubit states is locally distinguishable only if the summation of their
orthogonal Schmidt numbers is less than the total dimension $2^n$. When $n=2$
such a condition is also sufficient. Employing these results, we show that any
orthonormal basis of a subspace spanned by arbitrary three-qubit orthogonal
unextendible product bases (UPB) cannot be exactly distinguishable by local
operations and classical communication. This not only reveals another intrinsic
property of three-qubit orthogonal UPB, but also provides a class of locally
indistinguishable subspaces with dimension 4. We also explicitly construct
locally indistinguishable subspaces with dimensions 3 and 5, respectively. In
particular, 3 is the minimal possible dimension of locally indistinguishable
subspaces. Combining with the previous results, we conclude that any positive
integer between 3 and 7 is the possible dimension of some three-qubit locally
indistinguishable subspace.

Wu, X. & Duan, R. 2007, 'Exact Quantum Search by Parallel Unitary Discrimination Schemes'.

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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
$O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we
seek for the results about the exact algorithms, i.e. the ones succeed with
certainty. Under the standard oracle model $\sum_j (-1)^{\delta_{\tau j}}|j><
j|$, we demonstrate a tight lower bound ${2/3}N+o(N)$ of the number of queries
for any parallel scheme with unentangled input states. With the assistance of
entanglement, we obtain a general lower bound ${1/2}(N-\sqrt{N})$. We provide
concrete examples to illustrate our results. In particular, we show that the
case of N=6 can be solved exactly with only two queries by using a bipartite
entangled input state. Our results indicate that in the standard oracle model
the complexity of exact quantum search with one unique solution can be strictly
less than that of the calculation of OR function.

Ji, Z., Wang, G., Duan, R., Feng, Y. & Ying, M. 2006, 'Parameter estimation of quantum channels',

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*IEEE Trans. Inf. Theory*, vol. 54, p. 11.View/Download from: Publisher's site

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 non-unitary 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.

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. 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. 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

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. 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

Duan, R., Feng, Y. & Ying, M. 2006, 'Partial Recovery Of Quantum Entanglement',

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*IEEE Transactions On Information Theory*, vol. 52, no. 7, pp. 3080-3104.View/Download from: Publisher's site

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

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. 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

Duan, R., Ji, Z., Feng, Y. & Ying, M. 2006, 'Some Issues In Quantum Information Theory',

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*Journal Of Computer Science And Technology*, vol. 21, no. 5, pp. 776-789.View/Download from: Publisher's site

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. & Ying, M. 2005, 'Catalyst-Assisted Probabilistic Entanglement Transformation',

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*IEEE Transactions On Information Theory*, vol. 51, no. 3, pp. 1090-1101.View/Download from: Publisher's site

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. 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

Duan, R., Feng, Y., Ji, Z. & Ying, M. 2005, 'Efficiency Of Deterministic Entanglement Transformation',

*Physical Review A*, vol. 71, no. 2, pp. 1-7. 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., Li, X. & Ying, M. 2005, 'Multiple-Copy Entanglement Transformation And Entanglement Catalysis',

*Physical Review A*, vol. 71, no. 4, pp. 1-11. 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

Sun, X., Duan, R. & Ying, M. 2005, 'The Existence Of Quantum Entanglement Catalysts',

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*IEEE Transactions On Information Theory*, vol. 51, no. 1, pp. 75-80.View/Download from: Publisher's site

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., 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. 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

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. 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

Ji, Z., Duan, R. & Ying, M. 2004, 'Comparability of multipartite entanglement',

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*Phys. Lett. A*, vol. 330, pp. 418-423.View/Download from: Publisher's site

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

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. 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

Duan, R., Ji, Z., Feng, Y. & Ying, M. 2003, 'Quantum operation, quantum Fourier transform and semi-definite programming',

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*Phys. Lett. A 323(2004)48*.View/Download from: Publisher's site

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 this class of operations. A more
general class of operations on qudits is also considered and its completely
positive condition is reduced to the well-known semi-definite programming
problem.

Feng, Y., Zhang, S., Duan, R. & Ying, M. 2002, 'Lower Bound On Inconclusive Probability Of Unambiguous Discrimination',

*Physical Review A*, vol. 66, no. 6, pp. 1-4. We derive a lower bound on the inconclusive probability of unambiguous discrimination among n linearly independent quantum states by using the constraint of no signaling. It improves the bound presented in the. paper of Zhang, Feng, Sun, and Ying [Phys.