Purity distribution for generalized random Bures mixed states

摘要: We compute the distribution of purity for random density matrices (i.e.random mixed states) in a large quantum system, distributed according to Bures measure. The full is computed using mapping matrix theory and then Coulomb gas method. find three regimes that correspond two phase transitions associated gas. first transition characterized by an explosion third derivative on left point. second order, it detachement single charge A key remark this paper states are closely related O(n) model n=1. This actually led us study "generalized states" keeping $n$ general instead specializing