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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This work is supported by NSFC (Grant Nos. 61572081, 61672110, 61402148).
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Xu, GB., Wen, QY., Gao, F. et al. Local indistinguishability of multipartite orthogonal product bases. Quantum Inf Process 16, 276 (2017). https://doi.org/10.1007/s11128-017-1725-5
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DOI: https://doi.org/10.1007/s11128-017-1725-5