Local indistinguishability of orthogonal product states

Abstract

In the general bipartite quantum system $m\otimes n$, Wang \emph{et al.} [Y.-L Wang \emph{et al.}, Phys. Rev. A \textbf{92}, 032313 (2015)] presented $3(m+n)-9$ orthogonal product states which cannot be distinguished by local operations and classical communication (LOCC). In this paper, we aim to construct less locally indistinguishable orthogonal product states in $m\otimes n$. First, in $3\otimes n(3<n)$ quantum system, we construct $3n-2$ locally indistinguishable orthogonal product states which are not unextendible product bases. Then, for $m\otimes n(4\le m\le n)$, we present $3n+m-4$ orthogonal product states which cannot be perfectly distinguished by LOCC. Finally, in the general bipartite quantum system $m\otimes n(3\le m\le n)$, we show a smaller set with $2n-1$ orthogonal product states and prove that these states are LOCC indistinguishable using a very simple but quite effective method. All of the above results demonstrate the phenomenon of nonlocality without entanglement.

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• Distinguishability classes, resource sharing, and bound entanglement distribution
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• Bounds on the smallest sets of quantum states with special quantum nonlocality
• Locally distinguishing quantum states with limited classical communication
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• Genuine activation of nonlocality: From locally available to locally hidden information
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• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
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• 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
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• Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
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• More assistance of entanglement, less rounds of classical communication
• Exploring strong locality : Quantum state discrimination regime and beyond
• LOCC distinguishable orthogonal product states with least entanglement resource
• Locality of Orthogonal Product States via Multiplied Copies
• Unextendible and strongly uncompletable product bases
• The Independence of Distinguishability and the Dimension of the System
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• Local certification of unitary operations
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• Strong quantum nonlocality for multipartite entangled states