Detectors for local discrimination of sets of generalized Bell states

• URL: http://arxiv.org/abs/2504.11747v1
• Date: Wed, 16 Apr 2025 03:55:53 GMT
• Title: Detectors for local discrimination of sets of generalized Bell states
• Authors: Cai-Hong Wang, Jiang-Tao Yuan, Ying-Hui Yang, Mao-Sheng Li, Shao-Ming Fei, Zhi-Hao Ma,
• Abstract summary: A fundamental problem in quantum information processing is the discrimination among a set of quantum states under local operations and classical communication (LOCC)<n>In this work, we show how to determine all the detectors for a given generalized Bell states (GBS) set.<n>We show that for 4-GBS sets in quantum system $mathbbC6otimesmathbbC6$, the detectors are almost necessary for one-way LOCC distinguishability.
• Score: 1.1896943235396094
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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