Abstract
We show that every norm continuous one-parameter semigroup (ℐt: t ∈ ℝ+) of unital ultraweakly continuous completely positive maps on the algebra ℬ(ℋ0) of bounded operators on the separable infinite dimensional Hilbert space ℋ0 can be expressed as
where (j t : t ∈ ℝ+) is a quantum diffusion over ℬ(ℋ0) constructed using only one dimensional quantum stochastic calculus. In general the diffusion is not inner.
PS is supported by an SERC Research Studentship.
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Hudson, R.L., Shepperson, P. (1990). Stochastic dilations of quantum dynamical semigroups using one-dimensional quantum stochastic calculus. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications V. Lecture Notes in Mathematics, vol 1442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085514
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DOI: https://doi.org/10.1007/BFb0085514
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