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

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 $d$.

arXiv comment6 pages, presentation improved, final version

References in corpus (14)

• Local Distinguishability of Multipartite Orthogonal Quantum States
• Quantum State Discrimination
• Distinguishability of the Bell states
• Minimal conditions for local pure-state entanglement manipulation
• Distinguishability and indistinguishability by LOCC
• Local indistinguishability: more nonlocality with less entanglement
• Local indistinguishability and LOCC monotones
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Distinguishability of maximally entangled states
• Three maximally entangled states can require two-way LOCC for local discrimination
• Local copying and local discrimination as a study for non-locality of a set
• Detecting the local indistinguishability of maximally entangled states
• The local distinguishability of any three generalized Bell states
• Local unitary classification for sets of generalized Bell states

Cited by in corpus (5)

• Local discrimination of generalized Bell states via commutativity
• Detectors for local discrimination of sets of generalized Bell states
• Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability
• Local unitary classification of sets of generalized Bell states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• When quantum memory is useful for dense coding