Generalized perfect codes for symmetric classical-quantum channels
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/373658 |
| Acceso en línea: | https://hdl.handle.net/2117/373658 https://dx.doi.org/10.1109/TIT.2022.3170868 |
| Access Level: | acceso abierto |
| Palabra clave: | Quantum communication Error-correcting codes (Information theory) Codes Error probability Quantum channels Channel capacity Quantum system Task analysis Quantum state Comunicació quàntica Codis correctors d'errors (Teoria de la informació) Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Sumario: | 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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