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Foundations of Physics

A Mathematical Characterization of Quantum Gaussian Stochastic Evolution Schemes

David Cienfuegos Salgado, J. L. Sánchez‐Gómez, Miguel Ferrero

Published Feb 22, 2006• 0 citations
Publisher
DOI
10.1007/s10701-005-9034-8

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•Sep 23, 2020•1 citation
We give a complete characterization of the stochastic wave formalism when color Gaussian fluctuations are assumed. It is shown that in this case there is only one possible generalization of the stochastic wave dynamics, which is given by the ``non-Markovian quantum state diffusion model'' [Phys. Rev. A 58, 1699 (1998)]. Using functional techniques, we found an equivalent evolution in terms of the stochastic propagator. From this equation any controlled approximation can be constructed. The mean density-matrix evolution is given in a closed form. A relation with quantum master equations is established. An interaction parameter expansion and a small correlation time expansion are developed.
Several key properties of quantum evolutions are characterized by divisibility of the corresponding dynamical maps. In particular, a Markovian evolution respects CP-divisibility, whereas breaking of P-divisibility provides a clear sign of non-Markovian effects. We analyze a class of evolutions which interpolates between CP- and P-divisible classes and is characterized by dissipativity -- a long known but so far not widely used formal concept to classify open system dynamics. By making a connection to stochastic jump unravellings of master equations, we demonstrate that there exists inherent freedom in how to divide the terms of the underlying master equation into the deterministic and jump parts for the stochastic description. This leads to a number of different unravelings, each one with a measurement scheme interpretation and highlighting different properties of the considered open system dynamics. Starting from formal mathematical concepts, our results allow us to get fundamental insights in open system dynamics and to ease their numerical simulations.