Pengfei Liang

Exact quantum Bayesian rule for qubit measurements in circuit QED

  1. Wei Feng,
  2. Pengfei Liang,
  3. Lupei Qin,
  4. and Xin-Qi Li
Developing efficient and reliable schemes for practical quantum measurements is of essential importance to quantum information science and quantum metrology. In this work, for the increasingly
important superconducting circuit-QED setup, we present a rigorous approach starting with the quantum trajectory equation (QTE) to establish an {\it exact} quantum Bayesian rule. For the „realistic“ back-action (no qubit state information gain), we obtain important correction factors for arbitrary setup parameters. For the „spooky“ information gain back-action, we establish new prior distribution knowledge for the Bayesian inference, which differ from the standard Gaussian distribution and ensure to give strictly the same results as that by numerically integrating the QTE. Compared to the QTE approach, while keeping the same accuracy, the obtained quantum Bayesian rule has much higher efficiency to compute the stochastic change of the measured state. The generic method of this work opens also a new way to construct exact quantum Bayesian rules for quantum measurement in other systems.
arxiv pdf

Weak values in continuous weak measurement of qubits

  1. Lupei Qin,
  2. Pengfei Liang,
  3. and Xin-Qi Li
For continuous weak measurement of qubits, we obtain exact expressions for weak values (WVs) from the post-selection restricted average of measurement outputs, by using both the quantumtrajectory-
equation (QTE) and quantum Bayesian approach. The former is applicable to short-time weak measurement, while the latter can relax the measurement strength to finite. We find that even in the „very“ weak limit the result can be essentially different from the one originally proposed by Aharonov, Albert and Vaidman (AAV), in a sense that our result incorporates non-perturbative correction which could be important when the AAV’s WV is large. Within the Bayesian framework, we obtain also elegant expressions for finite measurement strength and find that the amplifier’s noise in quantum measurement has no effect on the WVs. In particular, we obtain very useful result for homodyne measurement in circuit-QED system, which allows for measuring the real and imaginary parts of the AAV’s WV by simply tuning the phase of the local oscillator. This advantage can be exploited as efficient state-tomography technique.
arxiv pdf