Binary Discrimination in Quantum Systems via Hypothesis Testing

Abstract

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 distinguish-ing 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 prob-ability 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.

References in corpus (8)

• Superconducting Circuits and Quantum Information
• A Straightforward Introduction to Continuous Quantum Measurement
• Bayesian parameter inference from continuously monitored quantum systems
• Proposal for detection of a single electron spin in a microwave resonator
• Single shot parameter estimation via continuous quantum measurement
• Hypothesis testing with open quantum systems
• Real-time quantum state estimation in circuit QED via Bayesian approach
• Discrimination of correlated and entangling quantum channels with selective process tomography