Correlation functions for realistic continuous quantum measurement

TL;DR

This paper derives an exact formula for the correlation functions of signals in continuous quantum measurement, accounting for realistic imperfections and applicable to both jump and diffusive quantum evolutions.

Contribution

It provides a self-contained derivation of correlation functions that depend on the initial state and SME, applicable to practical measurement scenarios.

Findings

Correlation functions depend on initial state and SME.

The formula applies to jump and diffusive evolutions.

Efficient numerical computation methods are presented.

Abstract

We propose a self-contained and accessible derivation of an exact formula for the $n$-point correlation functions of the signal measured when continuously observing a quantum system. The expression depends on the initial quantum state and on the Stochastic Master Equation (SME) governing the dynamics. This derivation applies to both jump and diffusive evolutions and takes into account common imperfections of realistic measurement devices. We show how these correlations can be efficiently computed numerically for commonly filtered and integrated signals available in practice.