The local indistinguishability of multipartite product states

TL;DR

This paper investigates the local indistinguishability of multipartite product states, providing new constructions and insights into how such states cannot be distinguished by LOCC in various quantum systems.

Contribution

It introduces a concise set of orthogonal product states in bipartite systems and offers explicit constructions for multipartite systems, enhancing understanding of local indistinguishability.

Findings

New set of $2n-1$ orthogonal product states in bipartite systems that are LOCC indistinguishable

Visual representation of indistinguishable states using 3D cubes in tripartite systems

Explicit construction method for indistinguishable product states in general multipartite systems

Abstract

In this paper, we mainly study the local indistinguishability of multipartite product states. Firstly, we follow the method of Z.-C. Zhang \emph{et al}[Phys. Rev. A 93, 012314(2016)] to give another more concise set of $2n-1$ orthogonal product states in $\mathbb{C}^m\otimes\mathbb{C}^n(4\leq m\leq n)$ which can not be distinguished by local operations and classical communication(LOCC). Then we use the 3 dimension cubes to present some product states which give us an intuitive view how to construct locally indistinguishable product states in tripartite quantum system. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite system.