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

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 $N\ge 3$. Based on this decomposition, we give explicit constructions of unextendible product bases in $N$-partite systems for odd $N\ge 3$. Furthermore, we apply our results to quantum secret sharing, uncompletable product bases, and PPT entangled states.

24 pages, 2 figures

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Cited by in corpus (6)

• Genuinely nonlocal sets without entanglement in multipartite systems
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Strongest quantum nonlocality in $N$-partite systems
• Activate genuine nonlocality from distinguishable sets in tripartite systems
• Global versus Local Discrimination of Locally Implementable Multipartite Unitaries
• Progress in the study of the (non)existence of genuinely unextendible product bases