Exact signal correlators in continuous quantum measurements

TL;DR

This paper derives an exact formula for signal correlation functions in continuous quantum measurements, enabling direct parameter estimation from experimental data without complex state reconstruction.

Contribution

It introduces a novel, exact formula for n-point correlation functions in continuous quantum measurements, applicable with detection imperfections, using stochastic calculus techniques.

Findings

Provides an exact, easily interpretable formula for signal correlators

Enables direct estimation of system parameters from experimental data

Connects continuous measurement theory with discrete interaction models

Abstract

This article provides an exact formula for the signal n-point correlation functions of detectors continuously measuring an arbitrary quantum system, in the presence of detection imperfections. The derivation uses only continuous stochastic calculus techniques, but the final result is easily understood from a discrete picture of repeated interactions with qubits or from a parallel with continuous matrix product states. This result provides a crude yet efficient a way to estimate system parameters directly from experimental data, without requiring non-linear state reconstruction.