Laboratoire de Physique Théorique
Toulouse - UMR 5152

We analyze various ensembles of random quantum states and review methods to obtain them numerically as well as to realize them in a realistic physical set up. Due to the measure concentration phenomenon a typical random pure state of a bi-partite system is almost maximally entangled. Taking various measures on the set of pure states one can induce by partial trace various probability measures in the set of mixed states on a reduced system. Recent results on random states generated according to the Bures measure and random graph states, which lead to Marchenko-Pastur or higher order Fuss-Catalan distributions of level density are reviewed.