Laboratoire de Physique Théorique
Toulouse - UMR 5152

In this seminar, we study the limit eigenvalue distributions of partial transpose of random quantum states. This problem was previously investigated by Aubrun, and Banica and Nechita. By using Wishart matrix, they showed that the limit distributions are the shifted semicircular distribution or the free difference of two free Poisson distributions depending on how the concerned spaces grow. We look into this problem directly via the Weingarten calculus and find three natural regimes. Two of them correspond to the above two cases, and the rest turns out to be a simple matrix model for the meander polynomials. This is a joint work with Piotr Sniady.