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Bures distance holds a special place among various distance measures due toits several distinguished features and finds applications in diverse problemsin quantum information theory. It is related to fidelity and, among otherthings, it serves as a bona fide measure for quantifying the separability ofquantum states. In this work, we calculate exact analytical results for themean root fidelity and mean square Bures distance between a fixed densitymatrix and a random density matrix, and also between two random densitymatrices. In the course of derivation, we also obtain spectral density forproduct of above pairs of density matrices. We corroborate our analyticalresults using Monte Carlo simulations. Moreover, we compare these results withthe mean square Bures distance between reduced density matrices generated usingcoupled kicked tops and find very good agreement.

Random density matrices: Analytical results for mean root fidelity and mean square Bures distance