Non-commutative Markov chains and multi-analytic operators

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Abstract

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.
Original languageEnglish
Pages (from-to)275-288
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume364
Issue number1
DOIs
Publication statusPublished - 01 Apr 2010

Keywords

  • Repeated interaction
  • Open quantum system
  • Non-commutative Markov chain
  • Multivariate operator theory
  • Row contraction
  • Outgoing Cuntz scattering system
  • Transfer function
  • Multi-analytic operator
  • Input–output formalism
  • Linear system
  • Quantum control
  • Observability
  • Scattering theory
  • Characteristic function

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