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DOE OSTI · 21501336

Quantum stochastic processes for maps on Hilbert C*-modules

Heo, Jaeseong·Ji, Un Cig
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Abstract

We discuss pairs ({phi}, {Phi}) of maps, where {phi} is a map between C*-algebras and {Phi} is a {phi}-module map between Hilbert C*-modules, which are generalization of representations of Hilbert C*-modules. A covariant version of Stinespring's theorem for such a pair ({phi}, {Phi}) is established, and quantum stochastic processes constructed from pairs ({l_brace}{phi}{sub t{r_brace}}, {l_brace}{Phi}{sub t{r_brace}}) of families of such maps are studied. We prove that the quantum stochastic process J={l_brace}J{sub t{r_brace}} constructed from a {phi}-quantum dynamical semigroup {Phi}={l_brace}{Phi}{sub t{r_brace}} is a j-map for the quantum stochastic process j={l_brace}j{sub t{r_brace}} constructed from the given quantum dynamical semigroup {phi}={l_brace}{phi}{sub t{r_brace}}, and that J is covariant if the {phi}-quantum dynamical semigroup {Phi} is covariant.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTINGALGEBRABANACH SPACEHILBERT SPACEMAPSMATHEMATICAL SPACEMATHEMATICSMECHANICSQUANTUM MECHANICSSPACESTOCHASTIC PROCESSES

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Heo, Jaeseong, Ji, Un Cig. 2011-05-15. Quantum stochastic processes for maps on Hilbert C*-modules. https://doi.org/10.1063/1.3582778

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