Strong quantum nonlocality with entanglement

TL;DR

This paper constructs the first sets of strongly nonlocal orthogonal entangled states in tripartite systems for all dimensions greater than or equal to three, demonstrating strong quantum nonlocality with entanglement.

Contribution

It provides the first explicit construction of strongly nonlocal entangled states in tripartite systems, solving an open problem and introducing entanglement-assisted discrimination protocols.

Findings

Existence of strongly nonlocal entangled bases in $d\otimes d\otimes d$ for all $d\geq 3

Construction based on Rubik's cube analogy

Protocols with reduced entanglement resources for local discrimination

Abstract

Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existence results for sets of strongly nonlocal orthogonal states are limited to product states. In this paper, based on the Rubik's cube, we give the first construction of such sets consisting of entangled states in $d\otimes d\otimes d$ for all $d\geq 3$. Consequently, we answer an open problem given by Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)], that is, orthogonal entangled bases that are strongly nonlocal do exist. Furthermore, we propose two entanglement-assisted protocols for local discrimination of our results. Each protocol consumes less entanglement resource than the teleportation-based protocol averagely. Our results exhibit the phenomenon of strong quantum nonlocality with entanglement.