Strong Quantum Nonlocality without Entanglement in Multipartite Quantum Systems

Abstract

In this paper, we generalize the concept of strong quantum nonlocality from two aspects. Firstly in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d\otimes {\mathbb{C}}^d$ quantum system, we present a construction of strongly nonlocal quantum states containing $6(d-1{)}^2$ orthogonal product states, which is one order of magnitude less than the number of basis states $d^3$. Secondly, we give the explicit form of strongly nonlocal orthogonal product basis in ${\mathbb{C}}^3\otimes {\mathbb{C}}^3\otimes {\mathbb{C}}^3\otimes {\mathbb{C}}^3$ quantum system, where four is the largest known number of subsystems in which there exists strong quantum nonlocality up to now. Both the two results positively answer the open problems in [Halder, \textit{et al.}, PRL, 122, 040403 (2019)], that is, there do exist and even smaller number of quantum states can demonstrate strong quantum nonlocality without entanglement.

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Cited by in corpus (32)

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• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality in $N$-partite systems
• Multiparty orthogonal product states with minimal genuine nonlocality
• Nonlocality without entanglement in general multipartite quantum systems
• 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
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• 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 $N$
• Nonlocality without entanglement: Party asymmetric case
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system
• Local discrimination of generalized Bell states via commutativity
• Strongest nonlocal sets with minimum cardinality in tripartite systems
• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
• Genuinely nonlocal sets without entanglement in multipartite systems
• Strong quantum nonlocality from hypercubes
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Exploring strong locality : Quantum state discrimination regime and beyond
• Strongest quantum nonlocality in $N$-partite systems
• Information locking and its resource efficient extraction
• Classifying locally distinguishable sets: No activation across bipartitions
• The construction of sets with strong quantum nonlocality using fewer states
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable 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