Non-Commutative Markov Chains and Multi-Analytic Operators

Details Non-Commutative Markov Chains and Multi-Analytic Operators Non-Commutative Markov Chains and Multi-Analytic Operators

2009-02-19

arxiv.org/abs/0902.3445v1

Physics

Mathematical Physics

19 pages

Scientific paper

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

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