Strong convergence of quantum random walks via semigroup decomposition

Alexander Belton; Michal Gnacik; J. M. Lindsay

doi:10.1007/s00023-018-0676-4

Strong convergence of quantum random walks via semigroup decomposition

Alexander Belton, Michal Gnacik, J. M. Lindsay

School of Mathematics & Physics

Lancaster University

Research output: Contribution to journal › Article › peer-review

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Abstract

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 language	English
Pages (from-to)	1711–1746
Number of pages	36
Journal	Annales Henri Poincaré
Volume	19
Issue number	6
Early online date	21 Apr 2018
DOIs	https://doi.org/10.1007/s00023-018-0676-4
Publication status	Published - 1 Jun 2018

Keywords

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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10.1007/s00023-018-0676-4

Convergence_of_quantum_random_walks_BGL
This is a post-peer-review, pre-copyedit version of an article published in Annales Henri Poincare on 21.04.2018. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00023-018-0676-4.
Accepted author manuscript (Post-print), 542 KB

Cite this

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Strong convergence of quantum random walks via semigroup decomposition

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Keywords

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