Finding out all locally indistinguishable sets of generalized Bell states

Abstract

In general, for a bipartite quantum system ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ and an integer $k$ such that $4\le k\le d$,there are few necessary and sufficient conditions for local discrimination of sets of $k$ generalized Bell states (GBSs) and it is difficult to locally distinguish $k$-GBS sets.The purpose of this paper is to completely solve the problem of local discrimination of GBS sets in some bipartite quantum systems.Firstly three practical and effective sufficient conditions are given,Fan${}^{,}$s and Wang et al.${}^{,}$s results [Phys Rev Lett 92, 177905 (2004); Phys Rev A 99, 022307 (2019)] can be deduced as special cases of these conditions.Secondly in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$, a necessary and sufficient condition for local discrimination of GBS sets is provided, and a list of all locally indistinguishable 4-GBS sets is provided,and then the problem of local discrimination of GBS sets is completely solved.In ${\mathbb{C}}^5\otimes {\mathbb{C}}^5$, a concise necessary and sufficient condition for one-way local discrimination of GBS sets is obtained,which gives an affirmative answer to the case $d=5$ of the problem proposed by Wang et al.

10 pages, 2 tables

References in corpus (2)

• Quantum secret sharing based on local distinguishability
• Detecting the local indistinguishability of maximally entangled states

Cited by in corpus (4)

• Detectors for local discrimination of sets of generalized Bell states
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
• Classical representation of local Clifford operators
• Application of Ramsey theory to localization of set of product states via multicopies