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.
Tres Observaciones sobre el Álgebra Lineal
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The Born Representation Theorem and the Unistochastic Theorem
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.