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Exact quantum Bayesian rule for qubit measurements in circuit QED.

Wei Feng1,2, Pengfei Liang2, Lupei Qin2

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This study presents an efficient quantum measurement framework for superconducting circuits. The new quantum Bayesian approach improves qubit state updates and enables advanced quantum analyses.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Condensed Matter Physics

Background:

  • Efficient quantum measurement frameworks are crucial for advancing quantum science and technology.
  • Superconducting circuit-Quantum Electrodynamics (circuit-QED) systems are vital platforms for quantum information processing.

Purpose of the Study:

  • To develop a rigorous and analytic solution for the effective quantum trajectory equation (QTE) in circuit-QED systems.
  • To generalize and improve existing quantum measurement approaches for enhanced accuracy and efficiency.

Main Methods:

  • Application of polaron transformation to the circuit-QED setup.
  • Conversion of the effective quantum trajectory equation to Stratonovich calculus.
  • Derivation of an analytic solution for the generalized quantum Bayesian approach.

Main Results:

  • An analytic solution for the effective QTE in circuit-QED systems is derived.
  • The solution generalizes the quantum Bayesian approach, improving qubit density matrix elements.
  • The updated method enhances output current probabilities and key phase factors.

Conclusions:

  • The new quantum Bayesian rule offers higher efficiency for updating measured states compared to numerical integration.
  • This framework facilitates more efficient analytical studies of quantum weak values, past quantum states, and quantum state smoothing.
  • The methodology provides a new pathway for deriving quantum Bayesian formulas for diverse and complex quantum systems.