Abstract
We studied the mutual information and quantum discord that Alice and Bob share when Bob implements a discrimination with a fixed rate of inconclusive outcomes (FRIO) onto two pure non-orthogonal quantum states, generated with arbitrary a priori probabilities. FRIO discrimination interpolates between minimum error (ME) and unambiguous state discrimination (UD). ME and UD are well known discrimination protocols with several applications in quantum information theory. FRIO discrimination provides a more general framework where the discrimination process together with its applications can be studied. In this setting, we compared the performance of optimum probability of discrimination, mutual information, and quantum discord. We found that the accessible information is obtained when Bob implements the ME strategy. The most (least) efficient discrimination scheme is ME (UD), from the point of view of correlations that are lost in the initial state and remain in the final state, after Bob’s measurement.
Highlights
During the last few decades, the classical and quantum correlations [1,2] present in quantum communication protocols have been an important subject of study [3,4,5,6]
We found that the most efficient discrimination scheme is minimum error (ME) (UD), from the point of view of quantum discord (QD) that is lost in the initial state and the mutual information (MI) that remains in the final state after the measurement
If we increase the rate of inconclusive outcomes, the success probability of discrimination decreases until it adopts its minimum value when Q = Qmax, which is associated with the case of unambiguous state discrimination (UD)
Summary
During the last few decades, the classical and quantum correlations [1,2] present in quantum communication protocols have been an important subject of study [3,4,5,6]. Bob could choose a particular quantum measurement in order to optimize some figure of merit, for instance, the mutual information, the Bayes cost, or the quantum correlations, among others [2,10,11] These quantities allow us to evaluate the performance of a signaldetection process [11], and, in this context, the study of quantum state discrimination strategies becomes crucial. The aim of this work is to study the success probability, and the mutual information (MI) that Alice and Bob share as well as the quantum discord (QD) involved in the scheme of FRIO discrimination This was done for two pure non-orthogonal states with arbitrary a priori probabilities, and it allows us to compare simultaneously the performance of ME, UD, and intermediate cases of FRIO discrimination using the aforementioned quantities.
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