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A general framework describing the statistical discrimination of an ensembleof quantum channels is given by the name of quantum reading. Several tools canbe applied in quantum reading to reduce the error probability in distinguishingthe ensemble of channels. Classical and quantum codes can be envisioned forthis goal. The aim of this paper is to present a simple but fruitful protocolfor this task using classical error-correcting codes. Three families of codesare considered: Reed-Solomon codes, BCH codes, and Reed-Muller codes. Inconjunction to the use of codes, we also analyze the role of the receiver. Inparticular, heterodyne and Dolinar receivers are taken in consideration. Theencoding and measurement schemes are connected by the probing step. As probe weconsider coherent states. In such simple manner, interesting results areobtained. As we show, for any fixed rate and code, there is a threshold underwhich using codes surpass optimal and sophisticated schemes. However, there arecodes and receiver schemes giving lower thresholds. BCH codes in conjunctionwith Dolinar receiver turn out to be the optimal strategy for error mitigationin the quantum reading task.

Error Probability Mitigation in Quantum Reading using Classical Codes