Bloch Equations and Completely Positive Maps

Details Bloch Equations and Completely Positive Maps Bloch Equations and Completely Positive Maps

2004-01-28

arxiv.org/abs/quant-ph/0401177v1

J. Mod. Optics 51, 1843 (2004)

Physics

Quantum Physics

Talk given at the Conference "Quantum Challenges", Falenty, Poland, September 4-7, 2003. 21 pages, 3 figures

Scientific paper

The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and colored stochastic noise.

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