Exact quantum Bayesian rule for qubit measurements in circuit QED

Abstract

Developing efficient framework for quantum measurements is of essential importance to quantum science and technology. In this work, for the important superconducting circuit-QED setup, we present a rigorous and analytic solution for the effective quantum trajectory equation (QTE) after polaron transformation and converted to the form of Stratonovich calculus. We find that the solution is a generalization of the elegant quantum Bayesian approach developed in arXiv:1111.4016 by Korotokov and currently applied to circuit-QED measurements. The new result improves both the diagonal and offdiagonal elements of the qubit density matrix, via amending the distribution probabilities of the output currents and several important phase factors. Compared to numerical integration of the QTE, the resultant quantum Bayesian rule promises higher efficiency to update the measured state, and allows more efficient and analytical studies for some interesting problems such as quantum weak values, past quantum state, and quantum state smoothing. The method of this work opens also a new way to obtain quantum Bayesian formulas for other systems and in more complicated cases.

7 pages, 2 figures

References in corpus (10)

• Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
• Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
• Quantum back-action of variable-strength measurement
• Weak values and the Leggett-Garg inequality in solid-state qubits
• Initialization by measurement of a two-qubit superconducting circuit
• Photon shell game in three-resonator circuit quantum electrodynamics
• Prediction and retrodiction for a continuously monitored superconducting qubit
• Quantum State Smoothing
• Quantum Bayesian rule for weak measurements of qubits in superconducting circuit QED
• Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing

Cited by in corpus (8)

• Quantum Bayesian approach to circuit QED measurement with moderate bandwidth
• Weak-value-amplification analysis beyond the AAV limit of weak measurements
• Non-equilibrium thermodynamics of continuously measured quantum systems: a circuit-QED implementation
• Qubit state tomography in superconducting circuit via weak measurements
• Real-time quantum state estimation in circuit QED via Bayesian approach
• Minimizing the discrimination time for quantum states of an artificial atom
• Estimation of parameters in circuit QED by continuous quantum measurement
• Gradual partial-collapse theory for ideal nondemolition measurements of qubits in circuit QED