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Using a circuit QED device, we present a theoretical study of real-timequantum state estimation via quantum Bayesian approach. Suitable conditionsunder which the Bayesian approach can accurately update the density matrix ofthe qubit are analyzed. We also consider the correlation between some basic andphysically meaningful parameters of the circuit QED and the performance of theBayesian approach. Our results advance the understanding of quantum Bayesianapproach and pave the way to study quantum feedback control and adaptivecontrol.

Real-time quantum state estimation in circuit QED via Bayesian approach