Strong quantum nonlocality in $N$-partite systems

TL;DR

This paper demonstrates the existence of strongly nonlocal sets of orthogonal entangled states in all multipartite systems with three or more parties, revealing new insights into quantum nonlocality beyond small systems.

Contribution

It proves the existence of strongly nonlocal sets in general N-partite systems for the first time, including genuinely entangled states with minimal size.

Findings

Strong nonlocality exists in all N-partite systems with N≥3.

Constructs smaller strongly nonlocal sets with genuinely entangled states for N=3,4.

Links strong nonlocality to local hiding of information.

Abstract

A set of multipartite orthogonal quantum states is strongly nonlocal if it is locally irreducible for every bipartition of the subsystems [Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four- and five-partite systems, the existence of strongly nonlocal sets in $N$-partite systems remains unknown when $N\geq 6$. In this paper, we successfully show that a strongly nonlocal set of orthogonal entangled states exists in $(\mathbb{C}^d)^{\otimes N}$ for all $N\geq 3$ and $d\geq 2$, which for the first time reveals the strong quantum nonlocality in general $N$-partite systems. For $N=3$ or $4$ and $d\geq 3$, we present a strongly nonlocal set consisting of genuinely entangled states, which has a smaller size than any known strongly nonlocal orthogonal product set. Finally, we connect strong quantum nonlocality with local hiding of information as an application.