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arXiv · 2110.08461

Strong quantum nonlocality from hypercubes

Fei Shi·Mao-Sheng Li·Mengyao Hu·Lin Chen·Man-Hong Yung·Yan-Ling Wang·Xiande Zhang
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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.

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Fei Shi, Mao-Sheng Li, Mengyao Hu, Lin Chen, Man-Hong Yung, Yan-Ling Wang, Xiande Zhang. 2021-10-16. Strong quantum nonlocality from hypercubes. https://arxiv.org/abs/2110.08461

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