Error Probability Mitigation in Quantum Reading using Classical Codes

A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed-Solomon codes, BCH codes, and Reed-Muller codes. In conjunction to the use of codes, we also analyze the role of the receiver. In particular, heterodyne and Dolinar receivers are taken in consideration. The encoding and measurement schemes are connected by the probing step. As probe we consider coherent states. In such simple manner, interesting results are obtained. As we show, for any fixed rate and code, there is a threshold under which using codes surpass optimal and sophisticated schemes. However, there are codes and receiver schemes giving lower thresholds. BCH codes in conjunction with Dolinar receiver turn out to be the optimal strategy for error mitigation in the quantum reading task.