Strong quantum nonlocality from hypercubes

Abstract

A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition. Most known constructions of strongly nonlocal orthogonal product set (OPS) are limited to tripartite systems, and they are lack of intuitive structures. In this work, based on the decomposition for the outermost layer of an n-dimensional hypercube for n = 3, 4, 5, we successfully construct strongly nonlocal OPSs in any possible three, four and five-partite systems, which answers an open question given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan et al.[Phys. Rev. A 102, 042228 (2020)] for any possible three, four and five-partite systems. Our results build the connection between hypercubes and strongly nonlocal OPSs, and exhibit the phenomenon of strong quantum nonlocality without entanglement in multipartite systems.

Strong quantum nonlocality for unextendible product bases in heterogeneous systems

“…In [44], the authors gave a decomposition for the outermost layer of 3,4-dimensional hypercubes, and our construction of UPBs in this paper is inspired by this decomposition. Since any OPS in 2 ⊗ n is locally reducible [12,33], a strongly nonlocal UPB in…”

“…For four-partite systems, strongly nonlocal UPBs are shown to exist in Supplementary material [59] by using the similar method. In [44], the authors gave a decomposition of the 5-dimensional hypercube, which may be used for constructing strongly nonlocal UPBs in any five-partite systems. However, it requires more calculations.…”

“…A strongly nonlocal OPS in d ⊗ d ⊗ d, d ⊗ d ⊗ (d + 1), 3 ⊗ 3 ⊗ 3 ⊗ 3 and 4 ⊗ 4 ⊗ 4 ⊗ 4 for d ≥ 3 was given in [43]. The authors in [44] constructed a strongly nonlocal OPS in [42,43] propose an open question: whether one can find strongly nonlocal UPBs? Specially, Ref.…”

Bounds on the smallest strong nonlocality set of multipartite quantum states

“…This motivates several works on this kind of strong quantum nonlocality (see Refs. [30][31][32][33][34][35][36]). All these results consider systems with at most five subsystems.…”

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

“…Most studies are focused on identifying sets of orthogonal product states or sets of the maximally entangled states. In addition, a stronger manifestation of nonlocality in multipartite systems has been studied which is based on the notion of local irreducibility in all biparitions of subsystems [68][69][70][71][72][73][74][75].…”