Using a circuit QED device, we present a theoretical study of real-time quantum state estimation via quantum Bayesian approach. Suitable conditions under which the Bayesian approach can accurately update the density matrix of the qubit are analyzed. We also consider the correlation between some basic and physically meaningful parameters of the circuit QED and the performance of the Bayesian approach. Our results advance the understanding of quantum Bayesian approach and pave the way to study quantum feedback control and adaptive control.

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We investigate the quantum parameter estimation in circuit quantum electrodynamics via dispersive measurement. Based on the Metropolis Hastings (MH) algorithm and the Markov chain Monte Carlo (MCMC) integration, a new algorithm is proposed to calculate the Fisher information by the stochastic master equation for unknown parameter estimation. Here, the Fisher information is expressed in the form of log-likehood functions and further approximated by the MCMC integration. Numerical results demonstrate that the single evolution of the Fisher information can probably approach the quantum Fisher information. The same phenomenon is observed in the ensemble evolution in the short time interval. These results demonstrate the effectiveness of the proposed algorithm.

We investigate the weak-force sensing in an optomechanical resonator by Kalman filter. By discretizing the continuous-time optomechanical system, the state of the resulting system is estimated by the unbiased minimum variance Kalman filter. Subsequently, the external stochastic force is estimated, provided that all noises in the system are white and Gaussian. Furthermore, the accuracy of force estimation, described by the mean squared error, is derived theoretically. The proposed algorithm is finally illustrated by comparing the theoretical accuracy with the numerical accuracy in an explicit example.

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We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguishing two Hamiltonians [Kiilerich and Mølmer, Phys. Rev. A, 98, 022103 (2018)]. Based on the measurement output and stochastic master equation, temporal evolutions of posterior probabilities of two hypotheses are given by Bayes' formula. The Bayes criterion is presented by the likelihood ratio conditioned on the outcome of measurements. Different from the calculation method based on maximum a posteriori criterion, the Bayes criterion based method for calculating the average probability of making errors is more suitable and efficient in general situation of binary discrimination. Finally, an example of distinguishing two candidate Hamiltonians is given and the running times of calculating the average probability of error under the Bayes criterion and the maximum a posteriori criterion are compared to illustrate the feasibility of the hypothesis testing in quickly distinguishing two candidates of the parameter to be estimated.

This paper investigates waveform estimation (tracking) of the time-varying force in a two-level optomechanical system with backaction noise by Kalman filtering. It is assumed that the backaction and measurement noises are Gaussian and white. By discretizing the continuous-time optomechanical system, the state of the resulting system can be estimated by the unbiased minimum variance Kalman filtering. Then an estimator of the time-varying force is obtained, provided that the external force is also in discrete time. Furthermore, the accuracy of the force estimation, described by the mean squared error, is derived theoretically. Finally, the feasibility of the proposed algorithm is illustrated by comparing the theoretical accuracy with the numerical accuracy in a numerical example.

We propose a W state-based protocol for anonymously transmitting quantum messages in a quantum network. Different from the existing protocols [A. Unnikrishnan, et al., Phys. Rev. Lett. 122, 240501 (2019)], the proposed protocol can be effectively implemented in the network only equipped with quantum channels and regular broadcast channels. Throughout the design procedure, we develop three sub-protocols using the W state, including the quantum collision detection protocol and the quantum notification protocol. Moreover, together with the conventional anonymous entanglement protocol, the whole anonymous communication protocol has been constructed. Finally, we examine the correctness and security of the proposed quantum anonymous communication protocol.