Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

Dahlem Center for Complex Quantum Systems,Freie Universitat Berlin, 14195 Berlin, Germany(Dated: June 20, 2014)We study quantum tomography based on a stochastic continuous-time measurement record ob-tained from a probe eld collectively interacting with an ensemble of identically prepared systems.In comparison to previous studies, we consider here the case in which the measurement-inducedbackaction has a nonnegligible e ect on the dynamical evolution of the ensemble. We formulatea maximum likelihood estimate for the initial quantum state given only a single instance of thecontinuous di usive measurement record. We apply our estimator to the simplest problem { statetomography of a single pure qubit, which, during the course of the measurement, is also subjectedto dynamical control. We identify a regime where the many-body system is well approximated at alltimes by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochas-tic evolution. We simulate the results of our estimator and show that we can achieve close to theupper bound of delity set by the optimal POVM. This estimate is compared to, and signi cantlyoutperforms, an equivalent estimator that ignores measurement backaction.