Genuinely nonlocal sets with smallest cardinality

TL;DR

This paper constructs the smallest known genuinely nonlocal sets of quantum states, demonstrating their existence in various multipartite systems and highlighting their complexity in quantum information access.

Contribution

It introduces genuinely nonlocal sets with minimal cardinality across different quantum states and systems, advancing understanding of nonlocality in quantum information.

Findings

Existence of genuinely nonlocal sets of three pure states in any N-partite system.

Existence of genuinely nonlocal sets of two mixed states regardless of copies.

Certain genuinely entangled states are necessary for nonlocality, complicating local access.

Abstract

Recently, there is growing interest in the study of genuine nonlocality, which serves to explore the local accessability of global information encoded in orthogonal multipartite quantum states under scenarios where not all subsystems are joined together. For such form of nonlocality, a probably most fundamental question is upon what states it is prone to be manifested. To tackle this, we present in this work genuinely nonlocal sets with the smallest possible cardinality. We first show the existence of genuinely nonlocal sets of three pure states in arbitrary N-partite system. As a byproduct, this also gives new examples of strongly nonlocal sets with dramatically smaller cardinality than ever for all possible systems, settling some related questions effortlessly. Then, for mixed hypothetical states, we show that genuinely nonlocal sets of two even exist, regardless of the number of copies available. In particular, it turns out for both our constructions that certain genuinely entangled states necessarily exist, nontrivially indicating their potential of raising difficulty in locally accessing multipartite quantum information.