Strong quantum nonlocality with entanglement

Abstract

Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existence results for sets of strongly nonlocal orthogonal states are limited to product states. In this paper, based on the Rubik's cube, we give the first construction of such sets consisting of entangled states in $d\otimes d\otimes d$ for all $d\ge 3$. Consequently, we answer an open problem given by Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)], that is, orthogonal entangled bases that are strongly nonlocal do exist. Furthermore, we propose two entanglement-assisted protocols for local discrimination of our results. Each protocol consumes less entanglement resource than the teleportation-based protocol averagely. Our results exhibit the phenomenon of strong quantum nonlocality with entanglement.

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Cited by in corpus (28)

• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality in $N$-partite systems
• Nonlocality without entanglement in general multipartite quantum systems
• Multiparty orthogonal product states with minimal genuine nonlocality
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Local distinguishability based genuinely quantum nonlocality without entanglement
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• Locally stable sets with minimum cardinality
• Orthogonal product sets with strong quantum nonlocality on plane structure
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system
• Strongest nonlocal sets with minimum cardinality in tripartite systems
• Local discrimination of generalized Bell states via commutativity
• Strong quantum nonlocality from hypercubes
• 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
• Strong nonlocal sets of UPB
• Strongest quantum nonlocality in $N$-partite systems
• Unextendible product operator basis
• The construction of sets with strong quantum nonlocality using fewer states
• Quantum permutation puzzles with indistinguishable particles
• The construction and local distinguishability of multiqubit unextendible product bases
• Graph connectivity based strong quantum nonlocality with genuine entanglement
• Activate genuine nonlocality from distinguishable sets in tripartite systems
• Application of Ramsey theory to localization of set of product states via multicopies