  We study random matrices acting on tensor product spaces which have been
transformed by a linear block operation. Using operator-valued free probability
theory, under some mild assumptions on the linear map acting on the blocks, we
compute the asymptotic eigenvalue distribution of the modified matrices in
terms of the initial asymptotic distribution. Moreover, using recent results on
operator-valued subordination, we present an algorithm that computes,
numerically but in full generality, the limiting eigenvalue distribution of the
modified matrices. Our analytical results cover many cases of interest in
quantum information theory: we unify some known results and we obtain new
distributions and various generalizations.
