Local indistinguishability of multipartite orthogonal product bases |
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Authors: | Guang-Bao Xu Qiao-Yan Wen Fei Gao Su-Juan Qin Hui-Juan Zuo |
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Affiliation: | 1.State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing,China;2.College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,China;3.College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang,China |
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Abstract: | So far, very little is known about local indistinguishability of multipartite orthogonal product bases except some special cases. We first give a method to construct an orthogonal product basis with n parties each holding a \(\frac{1}{2}(n+1)\)-dimensional system, where \(n\ge 5\) and n is odd. The proof of the local indistinguishability of the basis exhibits that it is a sufficient condition for the local indistinguishability of an orthogonal multipartite product basis that all the positive operator-valued measure elements of each party can only be proportional to the identity operator to make further discrimination feasible. Then, we construct a set of n-partite product states, which contains only 2n members and cannot be perfectly distinguished by local operations and classic communication. All the results lead to a better understanding of the phenomenon of quantum nonlocality without entanglement in multipartite and high-dimensional quantum systems. |
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