Parameter Estimation, Model Reduction and Quantum Filtering

Abstract

This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimator's uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback controller for continuous-time quantum error correction. Chapter 7 presents an exact model of symmetric processes of collective qubit systems.

254 pages, dissertation as submitted to the University of New Mexico, August 2009

References in corpus (10)

• Generalized Limits for Single-Parameter Quantum Estimation
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Quantum-limited metrology with product states
• Robust quantum parameter estimation: coherent magnetometry with feedback
• Collective processes of an ensemble of spin-1/2 particles
• Single shot parameter estimation via continuous quantum measurement
• The Langevin equation from Markovian Quantum Central Limits
• Efficient feedback controllers for continuous-time quantum error correction
• Universal quantum walks and adiabatic algorithms by 1D Hamiltonians