Abstract
After a short review of the notion of a quantum Markov chain, a particular class of such chains, generalizing in a natural way the usual random walks, is introduced. In Section (5) a limit theorem for quantum random walks is proved showing that the diffusion limit of the continuous coherent chain is an abelian extension of the Fock quantum Brownian motion on L 2(R+).
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Bibliography
L. Accardi Noncommutative Markov chains. In: international School of Mathematical Physics, Camerino (1974) 268–295.
L. Accardi On the noncommutative markovian property (in russian). Funkt. Anal. and its Appl. 9 (1975) 1–8.
L. Accardi Topics in quantum probability. Physics Reports 77 (1981) 169–192.
L.Accardi, A.Frigerio, J.Lewis Quantum stochastic processes Publications of the Research institute for Mathematical Sciences Kyoto University 18 (1982) 97–133.
L.Accardi, Bach A. The harmonic oscillator as quantum central limit of Bernoulli processes. Prob. Th. and Rel. Fields, to appear
Kruszinsky P. A problem in quantum probability preprint 1987
Louisell W.H. Radiation and noise in quantum electronics. McGraw-Hill (1964)
Sakai S. C*-algebras and W*-algebras. Springer 1971
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© 1989 Springer-Verlag
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Accardi, L., Watson, G.S. (1989). Quantum random walks. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083545
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DOI: https://doi.org/10.1007/BFb0083545
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