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Conditions for strictly purity-decreasing quantum Markovian dynamics

D. A. Lidar·A. Shabani·R. Alicki
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Abstract

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.

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D. A. Lidar, A. Shabani, R. Alicki. 2005-02-03. Conditions for strictly purity-decreasing quantum Markovian dynamics. https://doi.org/10.1016/j.chemphys.2005.06.038

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