Statistical properties of random density matrices

Abstract

Statistical properties of ensembles of random density matrices are\ninvestigated. We compute traces and von Neumann entropies averaged over\nensembles of random density matrices distributed according to the Bures\nmeasure. The eigenvalues of the random density matrices are analyzed: we derive\nthe eigenvalue distribution for the Bures ensemble which is shown to be broader\nthen the quarter--circle distribution characteristic of the Hilbert--Schmidt\nensemble. For measures induced by partial tracing over the environment we\ncompute exactly the two-point eigenvalue correlation function.\n