Local indistinguishability of orthogonal product states

TL;DR

This paper constructs smaller sets of orthogonal product states in bipartite quantum systems that cannot be distinguished by LOCC, highlighting nonlocality without entanglement.

Contribution

It presents new, smaller sets of LOCC-indistinguishable orthogonal product states in various bipartite systems, improving upon previous bounds.

Findings

Constructed $3n-2$ states in $3\otimes n$ systems

Presented $3n+m-4$ states in $m\otimes n$ systems for $4\leq m\leq n$

Proved $2n-1$ states are LOCC-indistinguishable in $m\otimes n$ systems with $3\leq m\leq n$

Abstract

In the general bipartite quantum system $m \otimes n$, Wang \emph{et al.} [Y.-L Wang \emph{et al.}, Phys. Rev. A \textbf{92}, 032313 (2015)] presented $3(m+n)-9$ orthogonal product states which cannot be distinguished by local operations and classical communication (LOCC). In this paper, we aim to construct less locally indistinguishable orthogonal product states in $m\otimes n $. First, in $3\otimes n (3< n)$ quantum system, we construct $3n-2$ locally indistinguishable orthogonal product states which are not unextendible product bases. Then, for $m\otimes n (4\leq m\leq n)$, we present $3n+m-4$ orthogonal product states which cannot be perfectly distinguished by LOCC. Finally, in the general bipartite quantum system $m\otimes n(3\leq m\leq n)$, we show a smaller set with $2n-1$ orthogonal product states and prove that these states are LOCC indistinguishable using a very simple but quite effective method. All of the above results demonstrate the phenomenon of nonlocality without entanglement.