Strong quantum nonlocality for multipartite entangled states

Abstract

Recently, Halder et al. (in Phys Rev Lett 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 with \(N\geqslant 3\). Finally, we also construct a class of strong nonlocality of orthogonal entangled states in \(d\otimes d\otimes \cdots \otimes d, d\geqslant 3\). Our results extend the concept of strong nonlocality for entangled states.