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

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

URL: http://arxiv.org/abs/2203.14503v3
Date: Sat, 11 May 2024 18:19:55 GMT
Title: Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
Authors: Yiyun He, Fei Shi, Xiande Zhang,
Abstract summary: The existence of strongly nonlocal product sets in multipartite systems remains unknown. We give explicit constructions of unextendible product bases in $N$-partite systems for odd $Ngeq 3$.
Score: 11.391485203897044
License: http://creativecommons.org/licenses/by/4.0/
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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