Quasifree stochastic calculus and quantum random walks

Alexander Belton, Michal Gnacik, J. Martin Lindsay, Ping Zhong

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Abstract

The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.
Original languageEnglish
Pages (from-to)1-39
Number of pages39
JournalJournal of Statistical Physics
Volume176
Issue number1
Early online date2 May 2019
DOIs
Publication statusPublished - Jul 2019

Keywords

  • Quantum stochastic calculus
  • quasifree representation
  • heat bath
  • repeated quantum interactions
  • toy Fock space
  • noncommutative Markov chain
  • quantum stochastic dilation
  • quantum dynamical semigroup
  • quantum Langevin equation

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