Multiparty orthogonal product states with minimal genuine nonlocality

TL;DR

This paper constructs genuinely nonlocal product states for any number of parties with minimal nonlocality, allowing perfect discrimination with minimal entanglement resources and revealing new insights into multipartite quantum nonlocality.

Contribution

It provides explicit constructions of genuinely nonlocal product states for arbitrary parties with minimal nonlocality, and analyzes their discrimination properties.

Findings

Genuinely nonlocal product states exist for any number of parties.

Perfect discrimination is possible with minimal entanglement resources.

Constructed states are fully separable but require complex measurements.

Abstract

Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. Concept of genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. Existence of such sets eventually motivates the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for arbitrary number of parties. Strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is possible with entangled resources residing in Hilbert spaces having the smallest possible dimensions. Our constructions lead to fully separable measurements that are impossible to implement even if all but one party come together. Furthermore, they also provide the opportunity to compare different multipartite states that otherwise are incomparable under single copy local manipulation.