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Random unistochastic matrices

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arxiv nlin/0112036 v3 pith:457AOA2X submitted 2001-12-20 nlin.CD

K. Zyczkowski , W. Slomczynski , M. Kus , H.-J. Sommers This is my paper · ORCID
classification nlin.CD
keywords matricesunistochasticensemblerandombistochasticcomplexorthogonalsymmetric
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An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and ortostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.

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Cited by 1 Pith paper

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  1. The Born Representation Theorem and the Unistochastic Theorem

    quant-ph 2026-08 conditional novelty 5.0 of 10

    Every finite stochastic matrix is a marginal of a larger unistochastic matrix, so classical Markov transitions can be represented by unitary quantum evolution with a fixed ancilla.

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