Strong quantum nonlocality for multipartite entangled states

TL;DR

This paper introduces a new concept of strong quantum nonlocality for multipartite entangled states, demonstrating that certain entangled states are locally indistinguishable across all bipartitions, thus exhibiting robust nonlocality.

Contribution

It provides a general definition of strong quantum nonlocality for entangled states and constructs explicit examples in various multipartite systems, extending previous nonlocality results.

Findings

Identifies strongly nonlocal entangled states in 2x2x2 systems.

Generalizes strong nonlocality to N-qubit systems with N≥3.

Constructs classes of strongly nonlocal states in higher-dimensional multipartite systems.

Abstract

Recently, Halder \emph{et al.} [S. Halder \emph{et al.}, Phys. Rev. Lett. \textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $2 \otimes 2 \otimes 2$ quantum system, we show that a set of orthogonal entangled states is locally reducible but locally indistinguishable in all bipartitions, which means the states have strong nonlocality. Furthermore, we generalize the result in N-qubit quantum system, where $N\geqslant 3$. Finally, we also construct a class of strong nonlocality of entangled states in $d\otimes d\otimes \cdots \otimes d, d\geqslant 3$. Our results extend the phenomenon of strong nonlocality for entangled states.