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Article

Замечания о квантовых марковских состояниях

Бежаева З. И., Оселедец В. И.

The definition of a quantum Markov state was given by Accardi. For the classical case, this definition gives hidden Markov measures, which, generally speaking, are not Markov measures. We can use a nonnegative transfer matrix to define a Markov measure. We use a positive semidefinite transfer matrix and select a class of quantum Markov states (in the sense of Accardi) on the quasilocal   C∗-algebras. An entangled quantum Markov state in the sense of Accardi and Fidaleo is a quantum Markov state in our sense. For the case where the transfer matrix has rank 1, we calculate the eigenvalues and the eigenvectors of the density matrices determining the quantum Markov state. The sequence of von Neumann entropies of the density matrices of this state is bounded.