Generalized perfect codes for symmetric classical-quantum channels
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Rights accessOpen Access
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ProjectAVANCES EN CODIFICACION Y PROCESADO DE SEÑAL PARA LA SOCIEDAD DIGITAL (AEI-PID2019-104958RB-C41)
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain N-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.
CitationBlasco, A.; Vázquez, G.; R. Fonollosa, J. Generalized perfect codes for symmetric classical-quantum channels. "IEEE transactions on information theory", Setembre 2022, vol. 68, núm. 9, p. 5923-5936.