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

TL;DR

This paper establishes a simple, necessary and sufficient criterion for the local distinguishability of sets of generalized Bell states in prime-dimensional quantum systems, simplifying the analysis of quantum state discrimination.

Contribution

It introduces a straightforward criterion that determines when sets of generalized Bell states in prime dimensions can be distinguished locally, advancing understanding in quantum information theory.

Findings

Criterion is necessary and sufficient for prime dimensions

Sets of d GBSs are distinguishable if conditions are met

Simplifies the process of checking local distinguishability

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 $d$.