Estimation of classical parameters via continuous probing of complementary quantum observables

Abstract

We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes to a Bayesian filter equation for the probability distribution of the desired parameters, and we illustrate its application by estimating the direction of a magnetic field. In our example, the field causes a ground state spin precession in a two-level atom which is detected by the polarization rotation of off-resonant optical probes, interacting with the atomic spin components.

11 pages, 4 figures (updated affiliation)

References in corpus (11)

• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Ziv-Zakai Error Bounds for Quantum Parameter Estimation
• Robust optimal quantum gates for Josephson charge qubits
• Microwave potentials and optimal control for robust quantum gates on an atom chip
• Bayesian parameter inference from continuously monitored quantum systems
• Single shot parameter estimation via continuous quantum measurement
• Qubit state monitoring by measurement of three complementary observables
• Atomic spin squeezing in an optical cavity
• Quantum filter reduction for measurement-feedback control via unsupervised manifold learning
• Decoherence and the conditions for the classical control of quantum systems
• Disentanglement of Source and Target and the Laser Quantum State

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