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    Approximate orthogonality of permutation operators, with application to quantum information by Harrow, Aram W.

    Published 2023
    “…This simple point has several applications in quantum information and random matrix theory: (1) showing that random maximally entangled states resemble fully random states, (2) showing that Boson sampling output probabilities resemble those from Gaussian matrices, (3) improving the Eggeling–Werner scheme for multipartite data hiding, (4) proving that the product test of Harrow–Montanaro cannot be performed using LOCC without a large number of copies of the state to be tested, (5) proving that the purity of a quantum state also cannot be efficiently tested using LOCC, and (6, published separately with Brandão and Horodecki) helping prove that poly-size random quantum circuits are poly-designs.…”
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