Limit distribution of partial transposition of block random matrices

Abstract

It is well known that, under some assumptions, the limit distribution of block random matrices and their partial transposition converges to the distributions of random variables in some non-commutative probability spaces. Using free probability theory, we obtain the relation between the free cumulants of the corresponding random variables. As an application, we can derive a new family of co-completely positive and [Formula: see text]-positive maps by using the Wishart ensemble.