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.

References in corpus (8)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski-Moriya interaction
• Quantum secret sharing based on local distinguishability
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Strong quantum nonlocality with entanglement
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Strong quantum nonlocality from hypercubes