  It is well known that, under some assumptions, the limit distribution of
random block matrices and their partial transposition converges to the
distributions of random variables in some noncommutative probability space.
Using free probability theory, we obtain the relation between the free
cumulants of the corresponding random variables. As an application, we are able
to derive a new family of co-completely positive and k-positive maps by using
the Wishart ensemble.

Quantum Physics