Strong quantum nonlocality in $N$-partite systems

• URL: http://arxiv.org/abs/2202.07139v1
• Date: Tue, 15 Feb 2022 02:19:46 GMT
• Title: Strong quantum nonlocality in $N$-partite systems
• Authors: Fei Shi, Zuo Ye, Lin Chen, and Xiande Zhang
• Abstract summary: We show that a strongly nonlocal set of entangled states exists in $(mathbbCd)otimes N$ for all $Ngeq 3$ and $dgeq 2$. We connect quantum nonlocality with local hiding of information as an application.
• Score: 16.790803450555885
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $N\geq 6$. In this paper, we successfully show that a strongly nonlocal set of orthogonal entangled states exists in $(\mathbb{C}^d)^{\otimes N}$ for all $N\geq 3$ and $d\geq 2$, which for the first time reveals the strong quantum nonlocality in general $N$-partite systems. For $N=3$ or $4$ and $d\geq 3$, 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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