Generalized Perfect Codes for Symmetric Classical-Quantum Channels

• URL: http://arxiv.org/abs/2007.07958v1
• Date: Wed, 15 Jul 2020 19:22:39 GMT
• Title: Generalized Perfect Codes for Symmetric Classical-Quantum Channels
• Authors: Andreu Blasco Coll, Gonzalo Vazquez-Vilar and Javier R. Fonollosa
• Abstract summary: We extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. For certain $N$-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect.
• Score: 9.797319790710711
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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