Parameter Estimation for Quantum Trajectories: Convergence Result

TL;DR

This paper rigorously proves the convergence of a parameter estimation method for quantum trajectories, providing theoretical validation and extending it to continuous parameters with an algorithm and simulations.

Contribution

It offers the first rigorous proof of convergence for a quantum parameter estimation method and proposes an algorithm for continuous parameters with supporting simulations.

Findings

Proves the consistency of the parameter estimation method.

Provides an algorithm for estimating continuous parameters.

Includes simulation results demonstrating the approach.

Abstract

A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an experimental perspective, these Kraus operators can depend on unknown physical parameters p. An interesting and powerful method has been proposed in [1] to estimate a parameter in a finite set; however, complete results of convergence were lacking. This article fills this gap by rigorously showing the consistency of the method, whereas there was only numerical evidence so far. When the parameter belongs to a continuous set, we propose an algorithm to approach its value and show simulation results.