Classical Tracking for Quantum Trajectories

TL;DR

This paper demonstrates that classical particle filtering techniques can effectively track quantum states in systems undergoing continuous measurement, especially at higher temperatures where quantum estimation is computationally intensive.

Contribution

It introduces the use of classical tracking methods, like particle filters, for quantum state estimation in experimentally realizable systems, bridging classical and quantum estimation techniques.

Findings

Classical particle filters can track quantum states effectively.

Classical tracking is advantageous at higher temperatures.

The approach reduces computational demands for quantum state estimation.

Abstract

Quantum state estimation, based on the numerical integration of stochastic master equations (SMEs), provides estimates for the evolution of quantum systems subject to continuous weak measurements. The approach is similar to classical state estimation methods in that the quantum trajectories produced by solving the SME are conditioned on continuous classical measurement signals. In this paper, we explore the use of classical state estimation for a candidate quantum system, one based on an experimentally realisable system: a material object undergoing continuous feedback cooling in an optical trap. In particular, we demonstrate that classical tracking methods based on particle filters can be used to track quantum states, and are particularly useful for higher temperature regimes where quantum state estimation becomes computationally demanding.