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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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