Nonlocality of orthogonal product basis quantum states

TL;DR

This paper investigates the local indistinguishability of orthogonal product basis quantum states in high-dimensional bipartite systems, revealing new minimal sets that are indistinguishable by LOCC but distinguishable by separable measurements.

Contribution

It constructs smaller sets of orthogonal product states that are LOCC indistinguishable and demonstrates the separation between LOCC and separable measurement capabilities.

Findings

Found a subset of 6d-9 states in odd-dimensional systems that are locally indistinguishable.

Generalized the construction to arbitrary bipartite systems, creating sets with 3(m+n)-9 states.

Proved these sets are LOCC indistinguishable but distinguishable by separable operations.

Abstract

We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of $\mathbb{C}^d\otimes\mathbb{C}^d$, where $d$ is odd, Zhang \emph{et al} have constructed $d^2$ orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. {\bf 90}, 022313(2014)]. We find a subset contains with $6d-9$ orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system $\mathbb{C}^m\otimes\mathbb{C}^n$. We present a small set with only $3(m+n)-9$ orthogonal product states and prove these states are LOCC indistinguishable. Even though these $3(m+n)-9$ product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.