Strong quantum nonlocality in $N$-partite systems

Abstract

A set of multipartite orthogonal quantum states is strongly nonlocal if it is locally irreducible for every bipartition of the subsystems [Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four- and five-partite systems, the existence of strongly nonlocal sets in $N$-partite systems remains unknown when $N\ge 6$. In this paper, we successfully show that a strongly nonlocal set of orthogonal entangled states exists in $({\mathbb{C}}^d{)}^{\otimes N}$ for all $N\ge 3$ and $d\ge 2$, which for the first time reveals the strong quantum nonlocality in general $N$-partite systems. For $N=3$ or $4$ and $d\ge 3$, we present a strongly nonlocal set consisting of genuinely entangled states, which has a smaller size than any known strongly nonlocal orthogonal product set. Finally, we connect strong quantum nonlocality with local hiding of information as an application.

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Cited by in corpus (11)

• Bounds on the smallest sets of quantum states with special quantum nonlocality
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• Locally stable sets with minimum cardinality
• Orthogonal product sets with strong quantum nonlocality on plane structure
• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Unextendible and uncompletable product bases in every bipartition
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• Strongest nonlocal sets with minimum cardinality in tripartite systems
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• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Strongest quantum nonlocality in $N$-partite systems