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:2112.14424 · Physical Review A

Bound on local minimum-error discrimination of bipartite quantum states

Donghoon Ha, Jeong San Kim

Published Mar 10, 2022• 8 citations
arXivHTMLPDF

Abstract

We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to realize the upper bound. We further establish a necessary and sufficient condition for this upper bound to be saturated. Finally, we illustrate our results using an example.

DOI
10.1103/physreva.105.032421

Related papers

Bound on optimal local discrimination of multipartite quantum states

Donghoon Ha, Jeong San Kim

We consider the unambiguous discrimination of multipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition to realize the upper bound. We further establish a necessary and sufficient condition for this upper bound to be saturated. Finally, we illustrate our results using examples in multidimensional multipartite quantum systems.

arXiv:2204.12830•Scientific Reports•Aug 19, 2022•3 citations

Upper and lower bounds on optimal success probability of quantum state discrimination with and without inconclusive results

Kenji Nakahira, Tsuyoshi Sasaki Usuda, Kentaro Kato

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state discrimination problem. We also give a necessary and sufficient condition for the upper bound to achieve the maximum success probability; the proposed lower bound can be obtained from this condition. It is derived that a slightly modified version of the proposed upper bound is tighter than that proposed by Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and lower bounds on the maximum success probability with a fixed rate of inconclusive results. The performance of the proposed bounds is evaluated through numerical experiments.

arXiv:1601.06231•Physical Review A•Jan 8, 2018•2 citations

Unambiguous discrimination of linearly independent pure quantum states: Optimal average probability of success

Somshubhro Bandyopadhyay

We consider the problem of unambiguous (error-free) discrimination of $N$ linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive an upper bound on the optimal average probability of success using a result on optimal local conversion between two bipartite pure states. We prove that for any $N\ensuremath{\ge}2$ an optimal measurement in general saturates our bound. In the exceptional cases we show that the bound is tight, but not always optimal.

arXiv:1404.3574•Physical Review A•Sep 5, 2014•12 citations

Bipartite quantum state discrimination and decomposable entanglement witness

Donghoon Ha, Jeong San Kim

We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the concept of decomposable entanglement witness, we establish conditions on minimum-error discrimination by positive-partial-transpose measurements. We also provide conditions on the upper bound of the maximum success probability over all possible positive-partial-transpose measurements. Finally, we illustrate our results using examples of multidimensional bipartite quantum states.

arXiv:2212.10799•Physical Review A•May 16, 2023•3 citations

Entanglement witness and multipartite quantum state discrimination

Donghoon Ha, Jeong San Kim

Abstract We consider multipartite quantum state discrimination and show that the minimum-error discrimination by separable measurements is closely related to the concept of entanglement witness (EW). Based on the properties of EW, we establish some necessary and/or sufficient conditions on minimum-error discrimination by separable measurements. We also provide some conditions on the upper bound of the maximum success probability over all possible separable measurements. Our results are illustrated by examples of multidimensional multipartite quantum states. Finally, we provide a systematic way in terms of the EW to construct multipartite quantum state ensembles showing nonlocality in state discrimination.

arXiv:2301.05420•Journal of Physics A Mathematical and Theoretical•Apr 13, 2023•2 citations

General lower and upper bounds under minimum-error quantum state discrimination

Elena R. Loubenets

For the optimal success probability under minimum-error discrimination between $r\ensuremath{\ge}2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations between these new general bounds and the known general bounds, lower and upper. We also present the example where the values of the new general lower and upper bounds on the optimal success probability are tighter than the values of most of the general analytical bounds known in the literature. The new upper bound on the optimal success probability explicitly generalizes to $r>2$ the form of the Helstrom bound. For $r=2$, each of our new bounds, lower and upper, reduces to the Helstrom bound.

arXiv:2105.06076•Physical Review A•Mar 4, 2022•13 citations
We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to realize the upper bound. We further establish a necessary and sufficient condition for this upper bound to be saturated. Finally, we illustrate our results using an example.
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state discrimination problem. We also give a necessary and sufficient condition for the upper bound to achieve the maximum success probability; the proposed lower bound can be obtained from this condition. It is derived that a slightly modified version of the proposed upper bound is tighter than that proposed by Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and lower bounds on the maximum success probability with a fixed rate of inconclusive results. The performance of the proposed bounds is evaluated through numerical experiments.
We consider the problem of unambiguous (error-free) discrimination of NNN linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive an upper bound on the optimal average probability of success using a result on optimal local conversion between two bipartite pure states. We prove that for any $N\ensuremath{\ge}2$ an optimal measurement in general saturates our bound. In the exceptional cases we show that the bound is tight, but not always optimal.
We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the concept of decomposable entanglement witness, we establish conditions on minimum-error discrimination by positive-partial-transpose measurements. We also provide conditions on the upper bound of the maximum success probability over all possible positive-partial-transpose measurements. Finally, we illustrate our results using examples of multidimensional bipartite quantum states.
Abstract We consider multipartite quantum state discrimination and show that the minimum-error discrimination by separable measurements is closely related to the concept of entanglement witness (EW). Based on the properties of EW, we establish some necessary and/or sufficient conditions on minimum-error discrimination by separable measurements. We also provide some conditions on the upper bound of the maximum success probability over all possible separable measurements. Our results are illustrated by examples of multidimensional multipartite quantum states. Finally, we provide a systematic way in terms of the EW to construct multipartite quantum state ensembles showing nonlocality in state discrimination.
For the optimal success probability under minimum-error discrimination between $r\ensuremath{\ge}2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations between these new general bounds and the known general bounds, lower and upper. We also present the example where the values of the new general lower and upper bounds on the optimal success probability are tighter than the values of most of the general analytical bounds known in the literature. The new upper bound on the optimal success probability explicitly generalizes to r>2r>2r>2 the form of the Helstrom bound. For r=2r=2r=2, each of our new bounds, lower and upper, reduces to the Helstrom bound.