Optimal Discrimination of Two Nonorthogonal States by Continuous Probing and Feedback Operation. Issue 5 (30th March 2022) - Xu, Peng
Abstract: For a quantum system prepared probabilistically on two or more non‐orthogonal states, the observer cannot discriminate the initial preparation perfectly. Kurt Jacobs [ Quantum Inf. Comput . 2007, 7, 127] introduced a measurement operator that could increase the rate of information obtained using a continuous measurement scheme. However, the better effect happens at the expense of reducing the total information from the quantum system. To address this problem, an optimal operator that could yield the maximal value of mutual information for a long‐time measurement is found. Particularly, it turns out that the error probability is minimized for any measurement moment by measuring the optimal operator. Furthermore, for a given finite measurement time, a measurement scheme to maximize the obtained mutual information is presented. It is shown that while the Jacobs' operator should be used for a short‐time case, for a long‐time limit, the proposed optimal operator should be employed. For a given finite duration, the proposal could determine the optimal measurement operator that maximizes the final value of mutual information. Abstract : An optimal operator is found that could yield the maximal value of mutual information for a long‐time measurement. It turns out that the error probability is minimized for any measurement moment by measuring the optimal operator. For a given finite duration, the proposal could determine the optimal measurement operator that maximizes the final value of mutual information.