Detectors for local discrimination of sets of generalized Bell states

Fuente: arXiv
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Main Authors: Wang, Cai-Hong, Yuan, Jiang-Tao, Yang, Ying-Hui, Li, Mao-Sheng, Fei, Shao-Ming, Ma, Zhi-Hao
Format: Preprint
Published: 2025
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author Wang, Cai-Hong
Yuan, Jiang-Tao
Yang, Ying-Hui
Li, Mao-Sheng
Fei, Shao-Ming
Ma, Zhi-Hao
author_facet Wang, Cai-Hong
Yuan, Jiang-Tao
Yang, Ying-Hui
Li, Mao-Sheng
Fei, Shao-Ming
Ma, Zhi-Hao
contents A fundamental problem in quantum information processing is the discrimination among a set of orthogonal quantum states of a composite system under local operations and classical communication (LOCC). Corresponding to the LOCC indistinguishable sets of four ququad-ququad orthogonal maximally entangled states (MESs) constructed by Yu et al. [Phys. Rev. Lett. 109, 020506 (2012)], the maximum commutative sets (MCSs) were introduced as detectors for the local distinguishability of the set of generalized Bell states (GBSs), for which the detectors are sufficient to determine the LOCC distinguishability. In this work, we show how to determine all the detectors for a given GBS set. We construct also several 4-GBS sets without detectors, most of which are one-way LOCC indistinguishable and only one is one-way LOCC distinguishable, indicating that the detectors are not necessary for LOCC distinguishability. Furthermore, we show that for 4-GBS sets in quantum system $\mathbb{C}^{6}\otimes\mathbb{C}^{6}$, the detectors are almost necessary for one-way LOCC distinguishability, except for one set in the sense of local unitary equivalence. The problem of one-way LOCC discrimination of 4-GBS sets in $\mathbb{C}^{6}\otimes\mathbb{C}^{6}$ is completely resolved.
format Preprint
id arxiv_https___arxiv_org_abs_2504_11747
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Detectors for local discrimination of sets of generalized Bell states
Wang, Cai-Hong
Yuan, Jiang-Tao
Yang, Ying-Hui
Li, Mao-Sheng
Fei, Shao-Ming
Ma, Zhi-Hao
Quantum Physics
Mathematical Physics
81P18, 81P40, 81P48
A fundamental problem in quantum information processing is the discrimination among a set of orthogonal quantum states of a composite system under local operations and classical communication (LOCC). Corresponding to the LOCC indistinguishable sets of four ququad-ququad orthogonal maximally entangled states (MESs) constructed by Yu et al. [Phys. Rev. Lett. 109, 020506 (2012)], the maximum commutative sets (MCSs) were introduced as detectors for the local distinguishability of the set of generalized Bell states (GBSs), for which the detectors are sufficient to determine the LOCC distinguishability. In this work, we show how to determine all the detectors for a given GBS set. We construct also several 4-GBS sets without detectors, most of which are one-way LOCC indistinguishable and only one is one-way LOCC distinguishable, indicating that the detectors are not necessary for LOCC distinguishability. Furthermore, we show that for 4-GBS sets in quantum system $\mathbb{C}^{6}\otimes\mathbb{C}^{6}$, the detectors are almost necessary for one-way LOCC distinguishability, except for one set in the sense of local unitary equivalence. The problem of one-way LOCC discrimination of 4-GBS sets in $\mathbb{C}^{6}\otimes\mathbb{C}^{6}$ is completely resolved.
title Detectors for local discrimination of sets of generalized Bell states
topic Quantum Physics
Mathematical Physics
81P18, 81P40, 81P48
url https://arxiv.org/abs/2504.11747