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 (6)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Twin matter waves for interferometry beyond the classical limit
• Mixed-state fidelity and quantum criticality at finite temperature
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Parameter Estimation with Mixed-State Quantum Computation