Local distinguishability based genuinely quantum nonlocality without entanglement

Abstract

Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of the subsystems. As the difficulty of the problem, most of the results are restricted to tripartite systems. Here we consider a weaker form of nonlocality called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for every bipartition of the subsystems. In this work, we tend to study the latter form of nonlocality. First, we present an elegant set of product states in bipartite systems that is locally indistinguishable. After that, based on a simple observation, we present a general method to construct genuinely nonlocal sets of multipartite product states by using those sets that are genuinely nonlocal but with less parties. As a consequence, we obtain that genuinely nonlocal sets of fully product states exist for all possible multipartite quantum systems.

arXiv comment8 pages, 7 figures

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Cited by in corpus (12)

• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality in $N$-partite systems
• 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
• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Genuinely nonlocal sets without entanglement in multipartite systems
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Information locking and its resource efficient extraction
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Useful variants and perturbations of completely entangled subspaces and spans of unextendible product bases
• Activate genuine nonlocality from distinguishable sets in tripartite systems