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. A102, 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.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2101.00735

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• Strong quantum nonlocality in $N$-partite systems
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
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