Conditions for strictly purity-decreasing quantum Markovian dynamics

The purity, Tr(rho(2)), measures how pure or mixed a quantum state p 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. (c) 2005 Elsevier B.V. All rights reserved.