Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system

Abstract

Recently, much attention have been paid to the constructions of nonlocal multipartite orthogonal product states. Among the existing results, some are relatively complex in structure while others have many constraint conditions. In this paper, we firstly give a simple method to construct a nonlocal set of orthogonal product states in ${\otimes }_{j=1}^n{\mathbb{C}}^d$ for $d\ge 2$. Then we give an ingenious proof for local indistinguishability of the set constructed by our method. According to the characteristics of this construction method, we get a new construction of nonlocal set with fewer states in the same quantum system. Furthermore, we generalize these two results to a more general ${\otimes }_{i=1}^n{\mathbb{C}}^{d_j}$ quantum system for $d_j\ge 2$. Compared with the existing results, the nonlocal set of multipartite orthogonal product states constructed by our method has fewer elements and is more simpler.

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Cited by in corpus (20)

• Nonlocality without entanglement in general multipartite quantum systems
• Multiparty orthogonal product states with minimal genuine nonlocality
• 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
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Local discrimination of generalized Bell states via commutativity
• Strongest nonlocal sets with minimum cardinality in tripartite systems
• Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Unextendible and strongly uncompletable product bases
• Multi-partite subspaces containing no locally inaccessible information
• Entanglement witness and multipartite quantum state discrimination
• Application of Ramsey theory to localization of set of product states via multicopies
• Graph connectivity based strong quantum nonlocality with genuine entanglement
• Bounds on Multipartite Nonlocality via Reduction to Biased Nonlocality
• Nonlocal sets of orthogonal multipartite product states with less members