Abstract
A recent work by Mandarino, Linowski and Życzkowski left open the following question. If [Formula: see text] is a certain permutation of entries of an [Formula: see text] matrix (“mixing map”) and [Formula: see text] is an [Formula: see text] Haar unitary random matrix, then is the family [Formula: see text] asymptotically free? (Here by [Formula: see text] we understand the matrix resulted by permuting the entries of [Formula: see text] according to the permutation [Formula: see text].) This paper presents some techniques for approaching such problems. In particular, one easy consequence of the main result is that the question above has an affirmative answer.
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