Optimal Parameter Estimation for Quantum Markov Chains and IID Pure State Models - Godley, Alfred Elliot (2025)
This thesis presents several optimal estimation strategies for quantum parameter estimation, mostly applied to quantum Markov chains (QMCs) - discrete-time quantum open systems. Chapter 4, based on [78], solves the problem of optimal estimation of a QMC using adaptive measurements. This culminates in an algorithm that determines the optimal measurement basis for the next step of the QMC by tracking an object known as the measurement filter. Crucially, this involves only local measurements on the environment of the QMC; a considerable simplification in comparison to other optimal strategies. Additionally, this estimation scheme utilizes a coherent absorber. This is a secondary system that we use to post-process the quantum Markov chain before measurement, which we include to purify the stationary state of the QMC.