A sufficient condition for complete positivity

Date: 
Friday, February 6, 2015
Room: 
204
Speaker: 
Matteo Caiaffa
Abstract: 
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.
References: 
[1]H. P. Breuer and F. Petruccione. The Theory of Open Quantum Systems. Oxford University Press, Oxford, 2002, [2]A. Bassi and G. Ghirardi, “Dynamical reduction models,” Physics Reports, vol. 379, no. 5, pp. 257–426, 2003. [3]L. Diósi, “Comment on’uniqueness of the equation for quantum state vector collapse’[arxiv: 1303.4284],” arXiv preprint arXiv:1401.6197, 2014. [4]A. Barchielli and M. Gregoratti, Quantum trajectories and measurements in continuous time: the diffusive case, vol. 782. Springer, 2009 [5]F. Benatti and R. Floreanini, “Open quantum dynamics: complete positivity and entanglement,” International Journal of Modern Physics B, vol. 19, no. 19, pp. 3063–3139, 2005