Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0103111 · Physical Review A

Optimal conclusive discrimination of two nonorthogonal pure product multipartite states through local operations

Yi-Xin Chen, Dong Yang

Published Nov 13, 2001• 53 citations
arXivHTMLPDF

Abstract

We consider one copy of a quantum system prepared in one of two nonorthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols that achieve optimal conclusive discrimination by means of local operations and classical communications as good as by global measurements. Also, we show a protocol that minimizes the average number of local operations. Our result implies that two pure product multipartite states might not have the nonlocal property although more than two can have.

DOI
10.1103/physreva.64.064303

Related papers

Optimally conclusive discrimination of nonorthogonal entangled states by local operations and classical communications

Yi-Xin Chen, Dong Yang

We consider one copy of a quantum system prepared with equal prior probability in one of two nonorthogonal entangled states of multipartite distributed among separated parties. We demonstrate that these two states can be optimally distinguished in the sense of conclusive discrimination by local operations and classical communications alone. This proves strictly the conjecture that Virmani et al. confirmed numerically and analytically. Generally the optimal protocol requires local POVM operations which are explicitly constructed. The result manifests that distinguishable information is obtained only and completely at the last operation and all prior operations give no information about that state.

arXiv:quant-ph/0104068•Physical Review A•Jan 15, 2002•69 citations

Optimal conclusive discrimination of two states can be achieved locally

Zhengfeng Ji, Hongen Cao, Mingsheng Ying

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 ``nonlocality'' in the conclusive discrimination of two multipartite pure states.

arXiv:quant-ph/0407120•Physical Review A•Mar 18, 2005•43 citations

Quantum nonlocality without entanglement and state discrimination measures

Shayeef Murshid, Tathagata Gupta, Vincent Russo +1 more

An ensemble of product states is said to exhibit “quantum nonlocality without entanglement” if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.

arXiv:2506.20560•Quantum•Jul 23, 2026•0 citations

Local Distinguishability of Multipartite Orthogonal Quantum States

Jonathan Walgate, Anthony J. Short, Lucién Hardy +1 more

We consider one copy of a quantum system prepared in one of two orthogonal pure states, entangled or otherwise, and distributed between any number of parties. We demonstrate that it is possible to identify which of these two states the system is in by means of local operations and classical communication alone. The protocol we outline is both completely reliable and completely general; it will correctly distinguish any two orthogonal states 100% of the time.

arXiv:quant-ph/0007098•Physical Review Letters•Dec 4, 2000•474 citations

Discrimination of quantum states under locality constraints in the many-copy setting

Hao–Chung Cheng, Andreas Winter, Nengkun Yu

We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability, thus establishing the associated Chernoff exponent. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite asymptotic separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB.

IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•2 citations

Unambiguous discrimination of two nonorthogonal multipartite states using local measurements and classical communication (Invited Paper)

Jihane Mimih, Mark S. Hillery

We consider a quantum system of two nonorthogonal bipartite quantum states. We distribute the qubits between two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 23, 2005•0 citations
We consider one copy of a quantum system prepared in one of two nonorthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols that achieve optimal conclusive discrimination by means of local operations and classical communications as good as by global measurements. Also, we show a protocol that minimizes the average number of local operations. Our result implies that two pure product multipartite states might not have the nonlocal property although more than two can have.
We consider one copy of a quantum system prepared with equal prior probability in one of two nonorthogonal entangled states of multipartite distributed among separated parties. We demonstrate that these two states can be optimally distinguished in the sense of conclusive discrimination by local operations and classical communications alone. This proves strictly the conjecture that Virmani et al. confirmed numerically and analytically. Generally the optimal protocol requires local POVM operations which are explicitly constructed. The result manifests that distinguishable information is obtained only and completely at the last operation and all prior operations give no information about that state.
An ensemble of product states is said to exhibit “quantum nonlocality without entanglement” if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.
We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability, thus establishing the associated Chernoff exponent. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite asymptotic separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB.
We consider a quantum system of two nonorthogonal bipartite quantum states. We distribute the qubits between two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed.