Conditions for strictly purity-decreasing quantum Markovian dynamics
摘要
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.
引用
@article{arxiv.quant-ph/0411119,
title = {Conditions for strictly purity-decreasing quantum Markovian dynamics},
author = {D. A. Lidar and A. Shabani and R. Alicki},
journal= {arXiv preprint arXiv:quant-ph/0411119},
year = {2015}
}
备注
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 clarified