Local distinguishability based genuinely quantum nonlocality without entanglement

Abstract

Recently, Halder et al (2019 Phys. Rev. Lett. 122 040403) proposed the concept of strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of its subsystems. Due to the complexity of the problem, most results are limited to tripartite systems. Here we consider a weaker form of nonlocality which is called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for every bipartition of the subsystems. In this work, we study how to construct sets of orthogonal product states which are genuinely nonlocal. Firstly, we present a set of product states with simple structure in bipartite systems that is locally indistinguishable. After that, based on a simple observation, we present a general method to construct genuinely nonlocal sets of multipartite product states by using those sets that are genuinely nonlocal but with less parties. As a consequence, we obtain that genuinely nonlocal sets of fully product states exist in any L parties systems provided L ⩾ 3 and d i ⩾ 3 for all i.

Strong quantum nonlocality in $N$-partite systems

“…If any k "subordinates" are collusive, k < N , and they can only perform OPLMs, then the information will not be accessible at all. systems, then this set is said to be genuinely nonlocal [36,38]). Thus the information cannot be fully accessed by the subordinates even if any k subordinates are collusive, where k < N .…”

“…By using graph connectivity, Wang et al successfully constructed strongly nonlocal OGESs in C d ⊗ C d ⊗ C d [34]. The concept of strong quantum nonlocality was also extended to more general settings [35][36][37][38][39].…”

Quantum nonlocality without entanglement in a 2n-partite system

“…In 1999, Bennett et al [9] firstly presented an initial result by demonstrating a LOCC indistinguishable orthogonal product basis in C 3 ⊗ C 3 . Under their influence many orthogonal product sets with quantum nonlocality were provided in bipartite [10,11] and multipartite systems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Zhang et al [27] found a set of orthogonal product states which * Author to whom any correspondence should be addressed.…”

Strongly nonlocal unextendible product bases do exist

“…[43,44], the authors constructed some strongly nonlocal orthogonal entangled sets and bases in tripartite systems. Further, strong quantum nonlocality was generalized to more general settings [45][46][47]. Although many efforts have been made in the strong quantum nonlocality, the existence of strongly nonlocal UPBs remains unknown.…”