1 Department of Physics and Astronomy, Science and Technology, Aarhus University2 Teoretisk naturvidenskab, Aarhus University, Aarhus University3 Department of Physics and Astronomy, Science and Technology, Aarhus University
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.
Physical Review a (atomic, Molecular and Optical Physics), 2013, Vol 87, Issue 3