Single-shot parameter estimation via continuous quantum measurement

We present filtering equations for single-shot parameter estimation using continuous quantum measurement. By embedding parameter estimation in the standard quantum filtering formalism, we derive the optimal Bayesian filter for cases when the parameter takes on a finite range of values. Leveraging recent convergence results [R. van Handel, e-print arXiv:0709.2216], we give a condition which determines the asymptotic convergence of the estimator. For cases when the parameter is continuous valued, we develop quantum particle filters as a practical computational method for quantum parameter estimation.