A sufficient condition for complete positivity

Friday, February 6, 2015
Matteo Caiaffa
The evolution equations of the statistical operator are (often) subject to the natural request of complete positivity (CP). This property is guaranteed only if the master equation has a particular form, called Lindblad. When the Lindblad form is missing, the only way to check CP is to solve an eigenvalues problem, which in general is not a pleasant task. In order to find an easier condition to infer CP, we exploit the definition of completely positive dynamical maps. Then, by the mean of a certain commutativity property, we are allowed to work at the level of the wavefunction rather than that of the statistical operator.The result is that asking for a CP master equation is equivalent to the weaker request of having a norm preserving stochastic differential equation.
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