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arXiv · 2203.14503

Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$

Yiyun He·Fei Shi·Xiande Zhang
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Abstract

A set of orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. Although such a phenomenon has been shown to any three-, four-, and five-partite systems, the existence of strongly nonlocal orthogonal product sets in multipartite systems remains unknown. In this paper, by using a general decomposition of the $N$-dimensional hypercubes, we present strongly nonlocal orthogonal product sets in $N$-partite systems for all odd $N\geq 3$. Based on this decomposition, we give explicit constructions of unextendible product bases in $N$-partite systems for odd $N\geq 3$. Furthermore, we apply our results to quantum secret sharing, uncompletable product bases, and PPT entangled states.

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Yiyun He, Fei Shi, Xiande Zhang. 2022-03-28. Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$. https://doi.org/10.22331/q-2024-05-16-1349

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