Quantum Bayesian approach to circuit QED measurement with moderate bandwidth

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.

26 pages

References in corpus (19)

• Charge insensitive qubit design derived from the Cooper pair box
• Amplification and squeezing of quantum noise with a tunable Josephson metamaterial
• Controlling the spontaneous emission of a superconducting transmon qubit
• Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
• Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting
• Continuous quantum measurement and Itô formalism
• Observation of quantum jumps in a superconducting artificial atom
• Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
• Quantum back-action of variable-strength measurement
• Fast Reset and Suppressing Spontaneous Emission of a Superconducting Qubit
• Undoing a weak quantum measurement of a solid-state qubit
• Mapping the optimal route between two quantum states
• Continuous quantum measurement with independent detector cross-correlations
• Measuring a transmon qubit in circuit QED: dressed squeezed states
• Robust quantum state transfer using tunable couplers
• Quantum trajectories for the realistic measurement of a solid-state charge qubit
• Crossover of phase qubit dynamics in presence of negative-result weak measurement
• Coherence of a Josephson phase qubit under partial-collapse measurement
• Quantum Bayesian rule for weak measurements of qubits in superconducting circuit QED

Cited by in corpus (6)

• Incoherent qubit control using the quantum Zeno effect
• Probing quantumness with joint continuous measurements of non-commuting qubit observables
• Continuous measurements for control of superconducting quantum circuits
• Real-time quantum state estimation in circuit QED via Bayesian approach
• Past observable dynamics of a continuously monitored qubit
• Hybrid phase-space--Fock-space approach to evolution of a driven nonlinear resonator