Asymptotics of random density matrices

Ion Nechita (1)

1 ICJ - Institut Camille Jordan

We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide asymptotic results on the behavior of the eigenvalues of random density matrices, including convergence of the empirical spectral measure. We also study the largest eigenvalue (almost sure convergence and fluctuations).

Mots clés: random density matrix; Wishart ensemble

Domaines: Physique Quantique [quant-ph]

Ion Nechita. Asymptotics of random density matrices. Annales Henri Poincaré, 2007, 8 (8), pp.1521-1538. ⟨10.1007/s00023-007-0345-5⟩. ⟨hal-00131136v3⟩