Quantum Bayesian approach to circuit QED measurement with moderate bandwidth

TL;DR

This paper extends the quantum Bayesian approach to continuous measurement in circuit QED setups with moderate resonator bandwidth, providing a simple, accessible description of measurement back-action applicable beyond the bad cavity limit.

Contribution

It generalizes the quantum Bayesian framework to moderate bandwidth regimes by applying it to entangled qubit-resonator states, maintaining simplicity and accessibility.

Findings

Evolution equations remain the same but apply to entangled states

Accessible derivation using elementary quantum mechanics

Applicable beyond the bad cavity limit

Abstract

We consider continuous quantum measurement of a superconducting qubit in the circuit QED setup with a moderate bandwidth of the measurement resonator, i.e., when the "bad cavity" limit is not applicable. The goal is a simple description of the quantum evolution due to measurement, i.e., the measurement back-action. Extending the quantum Bayesian approach previously developed for the "bad cavity" regime, we show that the evolution equations remain the same, but now they should be applied to the entangled qubit-resonator state, instead of the qubit state alone. The derivation uses only elementary quantum mechanics and basic properties of coherent states, thus being accessible to non-experts.