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Conditions for strictly purity-decreasing quantum Markovian dynamics
The purity, Tr(rho^2), measures how pure or mixed a quantum state rho is. It
is well known that quantum dynamical semigroups that preserve the identity
operator (which we refer to as unital) are strictly purity-decreasing
transformations. Here we provide an almost complete characterization of the
class of strictly purity-decreasing quantum dynamical semigroups. We show that
in the case of finite-dimensional Hilbert spaces a dynamical semigroup is
strictly purity-decreasing if and only if it is unital, while in the infinite
dimensional case, unitality is only sufficient.Comment: 4 pages, no figures. Contribution to the special issue "Real-time
dynamics in complex quantum systems" of Chemical Physics in honor of Phil
Pechukas. v2: Simplified proof of theorem 1 and validity conditions clarifie
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