Extracting filtered signal statistics of continuously measured quantum systems

TL;DR

This paper introduces a deterministic method to analyze the steady state and statistical properties of continuously measured quantum systems, enabling efficient extraction of information useful for quantum sensing.

Contribution

A new deterministic approach for computing steady states and extracting signal statistics in continuously monitored quantum systems, especially effective without feedback.

Findings

Efficient steady state computation method for quantum systems.

Ability to extract full counting statistics, mutual information, and Fisher information.

Application to single-qubit and spin chain models.

Abstract

The joint state of a continuously monitored quantum system and the classical filtered measurement record has recently been shown to be described by a quantum Fokker-Planck master equation [Phys. Rev. Lett. 129, 050401 (2022)]. We present a deterministic approach to compute the steady state of the system and detector. The method is shown to become particularly efficient in the absence of feedback, which we exploit to develop a perturbative approach valid for weak feedback. We show that through this method we can extract the full counting statistics of the signal, the quantum-classical mutual information between system and signal, as well as the Fisher information of the signal, which can be used for sensing applications. Our results are illustrated with both single-qubit models, as well as the spin chains governed by the one-dimensional transverse field Ising model or the Lipkin-Meshkov-Glick model.