01220nas a2200145   4500000000100000000000100001008004100002100002200043700001900065700002200084245004900106856004700155490000700202520086500209       2016                            d1 aZbigniew Puchała1 aŁukasz Pawela1 aKarol Życzkowski00aDistinguishability of generic quantum states  uhttps://doi.org/10.1103/PhysRevA.93.0621120 v933 a<p>Properties of random mixed states of order N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N, due to the concentration of measure, the trace distance between two random states tends to a fixed number D&nbsp;=1/4+1/π, which yields the Helstrom bound on their distinguishability. To arrive at this result we apply free random calculus and derive the symmetrized Marchenko–Pastur distribution, which is shown to describe numerical data for the model of two coupled quantum kicked tops. Asymptotic values for the fidelity, Bures and transmission distances between two random states are obtained. Analogous results for quantum relative entropy and Chernoff quantity provide other bounds on the distinguishablity of both states in a multiple measurement setup due to the quantum Sanov theorem.</p>