Strong quantum nonlocality for unextendible product bases in heterogeneous systems

Abstract

A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper, we construct a series of UPBs with different large sizes in $d_A\otimes d_B\otimes d_C$ and $d_A\otimes d_B\otimes d_C\otimes d_D$ for $d_A,d_B,d_C,d_D\ge 3$, and we also show that these UPBs have strong quantum nonlocality, which answers an open question given by Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] and Yuan \emph{et al.} [Phys. Rev. A \textbf{102}, 042228 (2020)] for any possible three and four-partite systems. Furthermore, we propose an entanglement-assisted protocol to locally discriminate the UPB in $3\otimes 3\otimes 4$, and it consumes less entanglement resource than the teleportation-based protocol. Our results build the connection between strong quantum nonlocality and UPBs.

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• Bounds on the smallest sets of quantum states with special quantum nonlocality
• 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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• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Information locking and its resource efficient extraction
• Unextendible and strongly uncompletable product bases
• Constructing unextendible product bases from multiqubit ones
• Progress in the study of the (non)existence of genuinely unextendible product bases