Tomography of a continuously monitored qubit

Time continuous measurements have proven themselves to be useful in real-time tracking and feedback control of quantum systems. In our work, we theoretically investigate the state tomography of a superconducting qubit coupled to a resonator in the strong dispersive regime. When the qubit is continuously monitored, the evolution of the qubit-resonator system is characterized by a stochastic master equation. Our numerical exploration suggests the requirement of an additional spectroscopy drive for a successful tomography of the full qubit state. Finally, complemented by the Bayesian mean estimation procedure, we reconstruct the state of the qubit conditioned on the measurement outcomes. Our analysis provides insights into the state estimation of a continuously monitored system and bears direct relevance for circuit QED experiments.