Bayesian parameter inference from continuously monitored quantum systems

Abstract

We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master equations describing the dynamics of a quantum system subject to a definite set of measurements provides likelihood functions for unknown parameters in the system dynamics, and we show that the estimation error, given by the Fisher information, can be identified by stochastic master equation simulations. For large parameter spaces we describe and illustrate the efficient use of Markov Chain Monte Carlo sampling of the likelihood function.

10 pages, 5 figures

References in corpus (17)

• Quantum-enhanced measurements: beating the standard quantum limit
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Twin matter waves for interferometry beyond the classical limit
• Quantum noise limited and entanglement-assisted magnetometry
• Sensing remote nuclear spins
• Quantum Trajectories and Quantum Measurement Theory
• Mixed-state fidelity and quantum criticality at finite temperature
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Sensing distant nuclear spins with a single electron spin
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• High Bandwidth Atomic Magnetometery with Continuous Quantum Non-demolition Measurements
• Linear stochastic wave-equations for continuously measured quantum systems
• State and dynamical parameter estimation for open quantum systems
• Parameter Estimation with Mixed-State Quantum Computation
• Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates
• Magnetometry with entangled atomic samples
• Analyzing quantum jumps of one and two atoms strongly coupled to an optical cavity

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