Nonlocality of orthogonal product basis quantum states

Abstract

We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$, where $d$ is odd, Zhang \emph{et al} have constructed $d^2$ orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. {\bf 90}, 022313(2014)]. We find a subset contains with $6d-9$ orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system ${\mathbb{C}}^m\otimes {\mathbb{C}}^n$. We present a small set with only $3(m+n)-9$ orthogonal product states and prove these states are LOCC indistinguishable. Even though these $3(m+n)-9$ product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.

5 pages

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• Vector Representations of Graphs and Distinguishing Quantum Product States with One-way LOCC
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• Locality of Orthogonal Product States via Multiplied Copies
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• The Independence of Distinguishability and the Dimension of the System
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• Graph connectivity based strong quantum nonlocality with genuine entanglement