Repeated Quantum Interactions and Unitary Random Walks
Attal, Stéphane; Dhahri, Ameur (2010), Repeated Quantum Interactions and Unitary Random Walks, Journal of Theoretical Probability, 23, 2, p. 345-361. http://dx.doi.org/10.1007/s10959-010-0281-z
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00199955/en/Date
2010Journal name
Journal of Theoretical ProbabilityVolume
23Number
2Publisher
Springer
Pages
345-361
Publication identifier
Metadata
Show full item recordAbstract (EN)
Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in $\RR^N$. The characterization we obtain is entirely algebraical in terms of the unitary operator driving the elementary interaction. We show that the solutions of these equations are then random walks on the group $U(\rH_0)$ of unitary operators on $\rH_0$.Subjects / Keywords
Obtuse random walks; Repeated quantum interactions; Classical and quantum noisesRelated items
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