Continuous quantum measurement for general Gaussian unravelings can exist

TL;DR

This paper demonstrates that continuous quantum measurements can be interpreted for a broad class of Gaussian non-Markovian models, including spin-boson and quantum Brownian motion, under specific noise covariance conditions.

Contribution

It establishes conditions under which Gaussian unravelings in non-Markovian quantum systems admit a measurement interpretation, expanding understanding of quantum measurement theory.

Findings

Measurement interpretation is possible when the Gaussian noise covariance satisfies a delta-function constraint.

The class includes models like spin-boson and quantum Brownian motion with colored baths.

Reduced states generally lack a closed master equation due to quantum memory effects.

Abstract

Quantum measurements and the associated state changes are properly described in the language of instruments. We investigate the properties of a time continuous family of instruments associated with the recently introduced family of general Gaussian non-Markovian stochastic Schr\"odinger equations. In this Letter we find that when the covariance matrix for the Gaussian noise satisfies a particular $\delta$-function constraint, the measurement interpretation is possible for a class of models with self-adjoint coupling operator. This class contains, for example the spin-boson and quantum Brownian motion models with colored bath correlation functions. Remarkably, due to quantum memory effects the reduced state, in general, does not have a closed form master equation while the unraveling has a time continuous measurement interpretation.