Symmetries of general non-Markovian Gaussian diffusive unravelings

Abstract

By using a condition of average trace preservation we rederive a general class of non-Markovian Gaussian diffusive unravelings [L. Diósi and L. Ferialdi, Phys. Rev. Lett. 113, 200403 (2014)], here valid for arbitrary non-Hermitian system operators and noise correlations. The conditions under which the generalized stochastic Schrödinger equation has the same symmetry properties (invariance under unitary changes of operator base) as a microscopic system-bath Hamiltonian dynamics are determined. While the standard quantum diffusion model (standard noise correlations) always shares the same invariance symmetry, the generalized stochastic dynamics can be mapped with an arbitrary bosonic environment only if some specific correlation constraints are fulfilled. These features are analyzed for different non-Markovian unravelings equivalent on average. Results based on quantum measurement theory that leads to specific cases of the generalized dynamics [J. Gambetta and H. M. Wiseman, Phys. Rev. A 66, 012108 (2002)] are studied from the perspective of the present analysis.