Parameter Estimation, Model Reduction and Quantum Filtering
arXiv:0908.1200
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 (38)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Mixed State Entanglement and Quantum Error Correction
- Quantum-enhanced measurements: beating the standard quantum limit
- Quantum metrology
- Decoherence Free Subspaces for Quantum Computation
- NMR Techniques for Quantum Control and Computation
- A Theory of Quantum Error-Correcting Codes
- Beating the Standard Quantum Limit with Four Entangled Photons
- Generation of Nonclassical Photon Pairs for Scalable Quantum Communication with Atomic Ensembles
- Generalized Limits for Single-Parameter Quantum Estimation
- Adaptive homodyne measurement of optical phase
- Continuous quantum error correction via quantum feedback control
- 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
- Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry
- Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble
- Full observation of single-atom dynamics in cavity QED
- Martingale Models for Quantum State Reduction
- Quantum-limited metrology with product states
- Continuous Weak Measurement and Nonlinear Dynamics in a Cold Spin Ensemble
- Robust quantum parameter estimation: coherent magnetometry with feedback
- Tensor polarizability and dispersive quantum measurement of multilevel atoms
- A practical scheme for error control using feedback
- Nonlinear quantum metrology using coupled nanomechanical resonators
- Collective processes of an ensemble of spin-1/2 particles
- Coherence-Preserving Quantum Bits
- Quantum limited measurements of atomic scattering properties
- Single shot parameter estimation via continuous quantum measurement
- The Langevin equation from Markovian Quantum Central Limits
- Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions
- Sensitivity optimization in quantum parameter estimation
- Polarization squeezing by optical Faraday rotation
- Efficient feedback controllers for continuous-time quantum error correction
- Derivation of Maxwell-Bloch-type equations by projection of quantum models
- Quantum error correction for continuously detected errors with any number of error channels per qubit
- Universal quantum walks and adiabatic algorithms by 1D Hamiltonians
- Scattering of polarized laser light by an atomic gas in free space: a QSDE approach
- Optimal error tracking via quantum coding and continuous syndrome measurement