Symmetries of general non-Markovian Gaussian diffusive unravelings

TL;DR

This paper derives a broad class of non-Markovian Gaussian diffusive unravelings with symmetry properties, analyzing conditions for their invariance and mapping to bosonic environments, advancing understanding of quantum measurement dynamics.

Contribution

It introduces a general framework for non-Markovian Gaussian diffusive unravelings with symmetry analysis and conditions for environmental mapping, extending previous models.

Findings

Standard quantum diffusion models always share symmetry invariance.

Generalized stochastic dynamics can be mapped to bosonic environments under specific correlations.

Analysis of measurement-based dynamics reveals conditions for symmetry preservation.

Abstract

By using a condition of average trace preservation we derive a general class of non-Markovian Gaussian diffusive unravelings [L. Diosi and L. Ferialdi, Phys. Rev. Lett. \textbf{113}, 200403 (2014)], here valid for arbitrary non-Hermitian system operators and noise correlations. The conditions under which the generalized stochastic Schrodinger equation has the same symmetry properties (invariance under unitary changes of operator base) than a microscopic system-bath Hamiltonian dynamics are determined. While the standard quantum diffusion model (standard noise correlations) always share 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 in average. Results based on quantum measurement theory that lead to specific cases of the generalized dynamics [J. Gambetta and H. M. Wiseman, Phys. Rev. A \textbf{66}, 012108 (2002)]\ are studied from the perspective of the present analysis.