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Conditions for strictly purity-decreasing quantum Markovian dynamics

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arxiv quant-ph/0411119 v2 pith:2G33WDPZ submitted 2004-11-16 quant-ph math-phmath.MPphysics.chem-ph

Conditions for strictly purity-decreasing quantum Markovian dynamics

D.A. Lidar (1) , A. Shabani (1) , R. Alicki (2) ((1) Center for Quantum Information , Quantum Control , University of Toronto , (2) Institute of Theoretical Physics , Astrophysics University of Gdansk) This is my paper
classification quant-ph math-phmath.MPphysics.chem-ph
keywords purity-decreasingquantumstrictlydynamicalcaseonlysemigroupsunital
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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