Local distinguishability of five orthogonal product states on bipartite and tripartite quantum systems

TL;DR

This paper investigates the local distinguishability of five orthogonal product states in bipartite and tripartite quantum systems, classifying their structures and determining conditions for LOCC distinguishability.

Contribution

It introduces the concept of orthogonal relation vectors, classifies five OPSs into categories, and analyzes their local distinguishability, advancing understanding of quantum nonlocality.

Findings

Five bipartite OPS categories can be perfectly distinguished by LOCC.

Six bipartite OPS structures are classified, with five distinguishable by LOCC.

Tripartite OPS structures are divided into eight categories with known distinguishability.

Abstract

Local distinguishability of orthogonal quantum states can effectively reduce the consumption of quantum resources and lower economic costs in quantum protocols. Although numerous achievements have been made regarding local distinguishability of orthogonal quantum states, some fundamental issues have not been effectively addressed. For example, the local distinguishability of five orthogonal product states (OPSs) is still unknown up to now. In this paper, we give the properties of local distinguishability of five OPSs on bipartite and tripartite quantum systems. Firstly, to characterize the structure of a set of bipartite OPSs, we propose the concept of the vector of orthogonal relations for a set of bipartite OPSs. Secondly, we classify the structures of five bipartite OPSs into six categories by this concept and prove that five of these six categories can be perfectly distinguished by local operations and classical communication (LOCC). Thirdly we show that the local distinguishability of each case of the sixth category singly. On the other hand, we first divide the structures of five tripartite OPSs into eight categories by the vectors of orthogonal relations of five tripartite OPSs. Then we give the local distinguishability of each category. Our work enriches the research results of quantum nonlocality and will provide a clear understanding of the local distinguishability of five OPSs.