Local distinguishability based genuinely quantum nonlocality without entanglement

TL;DR

This paper introduces a new form of quantum nonlocality called local distinguishability based genuine nonlocality, demonstrating the existence of such nonlocal sets of fully product states across all multipartite systems.

Contribution

It presents the first explicit construction of genuinely nonlocal sets of product states for all multipartite quantum systems, expanding understanding of quantum nonlocality without entanglement.

Findings

Genuinely nonlocal sets of product states exist in bipartite systems.

A general method to construct multipartite genuinely nonlocal sets from smaller sets.

Existence of genuinely nonlocal product states in all multipartite systems.

Abstract

Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of the subsystems. As the difficulty of the problem, most of the results are restricted to tripartite systems. Here we consider a weaker form of nonlocality called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for every bipartition of the subsystems. In this work, we tend to study the latter form of nonlocality. First, we present an elegant set of product states in bipartite systems that is locally indistinguishable. After that, based on a simple observation, we present a general method to construct genuinely nonlocal sets of multipartite product states by using those sets that are genuinely nonlocal but with less parties. As a consequence, we obtain that genuinely nonlocal sets of fully product states exist for all possible multipartite quantum systems.