Phys. Rev. A 99, 022114 (2019)
Estimation of parameters in circuit QED by continuous quantum measurement
Cheng Zhang1, Kai Zhou1, Wei Feng2, and Xin-Qi Li1,2,*
1Department of Physics, Beijing Normal University, Beijing 100875, China
2Center for Joint Quantum Studies, School of Science, Tianjin University, Tianjin 300072, China
Designing high-precision and efficient protocols is of crucial importance for quantum parameter estimation in practice. Estimation based on continuous quantum measurement is one possible type of this, which also appears to be the most natural choice for continuous dynamical processes. In this work we consider the state-of-the-art superconducting circuit quantum-electrodynamics (QED) systems, where high-quality continuous measurements have been extensively performed in the past decade. Within the framework of Bayesian estimation and particularly using the quantum Bayesian rule in circuit QED, we numerically simulate the likelihood function as an estimator for the Rabi frequency of qubit oscillations. We find that, by proper design of the interaction strength of measurement, the estimate precision can scale with the measurement time beyond the standard quantum limit, which is usually assumed for this type of continuous measurement. This unexpected result is supported by the simulated Fisher information and can be understood as a consequence of the quantum correlation between the output signals by simulating the effect of quantum efficiency of measurement.