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Inspired by the theory of quantum information, I use two non-Hermitian randommatrix models - a weighted sum of circular unitary ensembles and a product ofrectangular Ginibre unitary ensembles - as building blocks of three newproducts of random matrices which are generalizations of the Bures model. Iapply the tools of both Hermitian and non-Hermitian free probability tocalculate the mean densities of their eigenvalues and singular values in thethermodynamic limit, along with their divergences at zero; the results aresupported by Monte Carlo simulations. I pose and test conjectures concerningthe relationship between the two densities (exploiting the notion of theN-transform), the shape of the mean domain of the eigenvalues (an extension ofthe single ring theorem), and the universal behavior of the mean spectraldensity close to the domain's borderline (using the complementary errorfunction).

Generalized Bures products from free probability