Nonlocality without entanglement in general multipartite quantum systems

TL;DR

This paper introduces a new, efficient method for constructing nonlocal sets of orthogonal product states in multipartite quantum systems, demonstrating nonlocality without entanglement with fewer states than previous approaches.

Contribution

It presents a general construction for nonlocal orthogonal product states in multipartite systems, reducing the number of states needed to reveal nonlocality without entanglement.

Findings

Constructed nonlocal sets with fewer states than previous methods

Applicable to multipartite systems with arbitrary dimensions

Enhances understanding of nonlocality without entanglement

Abstract

The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon of nonlocality without entanglement more efficiently.