Strong convergence of quantum random walks via semigroup decomposition

Alexander Belton, Michal Gnacik, J. M. Lindsay

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We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.
Original languageEnglish
Pages (from-to)1711–1746
Number of pages36
JournalAnnales Henri Poincaré
Issue number6
Early online date21 Apr 2018
Publication statusPublished - 1 Jun 2018


  • Quantum random walks
  • repeated interactions
  • noncommutative Markov chains
  • toy Fock space
  • quantum stochastic cocycle
  • series product
  • quantum stochastic Trotter product
  • quantum stochastic calculus


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