Statistical properties of random density matrices

Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analysed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter-circle distribution characteristic of the Hilbert–Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.