Abstract
A necessary and sufficient condition is formulated for minimal quantum dynamical semigroups to be conservative. The paper also provides a Markovian dilation of the minimal semigroups, as a contractive solution of an associated quantum stochastic differential equation in Boson-Fock space, which is isometric if and only if the minimal semigroup is conservative. Using the reflection principle of Brownian motion a necessary and sufficient condition for the contractive solution to be co-isometric is also obtained.
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Mohari, A., Sinha, K.B. Stochastic dilation of minimal quantum dynamical semigroup. Proc Math Sci 102, 159–173 (1992). https://doi.org/10.1007/BF02837854
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DOI: https://doi.org/10.1007/BF02837854