Strong quantum nonlocality for unextendible product bases in heterogeneous systems

TL;DR

This paper constructs large unextendible product bases (UPBs) in multipartite systems that exhibit strong quantum nonlocality, answering open questions and proposing efficient local discrimination protocols with entanglement assistance.

Contribution

It introduces a series of UPBs with strong quantum nonlocality in multipartite systems, expanding understanding of nonlocality without entanglement and providing resource-efficient discrimination methods.

Findings

Constructed UPBs with strong nonlocality in systems with dimensions ≥3.

Answered open questions about strong nonlocality in UPBs for three and four-partite systems.

Proposed an entanglement-assisted protocol for local discrimination with less resource consumption.

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 $d_A, d_B, d_C, d_D\geq 3$, 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.