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The index of a quantum dynamical semigroup

William Arveson
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Abstract

A numerical index is introduced for semigroups of completely positive maps of $\Cal B(H)$ which generalizes the index of E_0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E_0-semigroup, provided that the dilation is minimal.

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William Arveson. 1997-05-25. The index of a quantum dynamical semigroup. https://arxiv.org/abs/funct-an/9705005

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