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Quantum Random Walks with General Particle States

Communications in Mathematical Physics volume 328, pages 573–596 (2014)Cite this article

Abstract

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This unifies and extends previous work on repeated-interactions models, including that of Attal and Pautrat (Ann Henri Poincaré 7:59–104 2006) and Belton (J Lond Math Soc 81:412–434, 2010; Commun Math Phys 300:317–329, 2010). When the random-walk generator acts by ampliation and either multiplication or conjugation by a unitary operator, it is shown that the quantum stochastic cocycle which arises in the limit is driven by a unitary process.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK

    Alexander C. R. Belton

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  1. Alexander C. R. Belton
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Correspondence to Alexander C. R. Belton.

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Communicated by A. Connes

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Belton, A.C.R. Quantum Random Walks with General Particle States. Commun. Math. Phys. 328, 573–596 (2014). https://doi.org/10.1007/s00220-014-1886-3

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  • DOI: https://doi.org/10.1007/s00220-014-1886-3

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