Simple criterion for local distinguishability of generalized Bell states in prime dimension

• URL: http://arxiv.org/abs/2102.07400v2
• Date: Mon, 24 May 2021 15:08:34 GMT
• Title: Simple criterion for local distinguishability of generalized Bell states in prime dimension
• Authors: T. Hashimoto, M. Horibe, and A. Hayashi
• Abstract summary: Local distinguishability of sets of generalized Bell states (GBSs) is investigated. We show that, if the space dimension $d$ is a prime, these conditions are necessary and sufficient for sets of $d$ GBSs in $mathbbCd otimes mathbbCd$ to be locally distinguishable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Local distinguishability of sets of generalized Bell states (GBSs) is investigated. We first clarify the conditions such that a set of GBSs can be locally transformed to a certain type of GBS set that is easily distinguishable within local operations and one-way classical communication. We then show that, if the space dimension $d$ is a prime, these conditions are necessary and sufficient for sets of $d$ GBSs in $\mathbb{C}^d \otimes \mathbb{C}^d$ to be locally distinguishable. Thus we obtain a simple computable criterion for local distinguishability of sets of $d$ GBSs in prime dimension $d$.

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