We study environmental decoherence for a quantum Markov semigroup T acting on an arbitrary von Neumann algebra M. In particular, we analyze the relationships between the decomposition of the algebra induced by decoherence and a sort of “isometric-sweeping decomposition” for the space of states. Moreover, when the semigroup has a faithful normal invariant state, we embed the algebra M in its completion \hat{M} with respect to the scalar product induced by the faithful state, and we compare the decomposition induced by decoherence with some other kind of isometric-sweeping decompositions of M and \hat{M}.
Environment induced decoherence for Markovian evolutions
SASSO, EMANUELA;UMANITA', VERONICA
2015-01-01
Abstract
We study environmental decoherence for a quantum Markov semigroup T acting on an arbitrary von Neumann algebra M. In particular, we analyze the relationships between the decomposition of the algebra induced by decoherence and a sort of “isometric-sweeping decomposition” for the space of states. Moreover, when the semigroup has a faithful normal invariant state, we embed the algebra M in its completion \hat{M} with respect to the scalar product induced by the faithful state, and we compare the decomposition induced by decoherence with some other kind of isometric-sweeping decompositions of M and \hat{M}.
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