Qubit measurement in circuit QED and the idea of one-step Bayesian state inference.
(a) Schematic plot for the circuit QED setup and measurement principle of qubit states via measuring the quadrature of the cavity field. The superconducting qubit couples dispersively to the cavity through Hamiltonian χa†aσz which, under the interplay of cavity driving and damping, forms cavity fields α1(t) and α2(t) corresponding to qubit states and . The leaked photon (with rate κ) is detected using the homodyne technique by mixing it with a local oscillator (LO). (b) Illustrative explanation for the advantage of the one-step Bayesian rule (BR) over the continuous (multi-step) integration of the quantum trajectory equation (QTE). That is, using the known functions α1,2(t) and the detected current I(t) of the homodyne measurement, the BR allows a one-step inference for the qubit state.