A unification of the coding theory and OAQEC perspective on hybrid codes

• URL: http://arxiv.org/abs/1806.03702v2
• Date: Mon, 7 Aug 2023 19:09:10 GMT
• Title: A unification of the coding theory and OAQEC perspective on hybrid codes
• Authors: Shayan Majidy
• Abstract summary: simultaneously transmitting both classical and quantum information over a quantum channel. The characterization of hybrid codes has been performed from a coding theory perspective and an operator algebra quantum error correction (OAQEC) perspective. We construct an example of a non-trivial degenerate 4-qubit hybrid code.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: There is an advantage in simultaneously transmitting both classical and quantum information over a quantum channel compared to sending independent transmissions. The successful implementation of simultaneous transmissions of quantum and classical information will require the development of hybrid quantum-classical error-correcting codes, known as hybrid codes. The characterization of hybrid codes has been performed from a coding theory perspective and an operator algebra quantum error correction (OAQEC) perspective. First, we demonstrate that these two perspectives are equivalent and that the coding theory characterization is a specific case of the OAQEC model. Second, we include a generalization of the quantum Hamming bound for hybrid error-correcting codes. We discover a necessary condition for developing non-trivial hybrid codes -- they must be degenerate. Finally, we construct an example of a non-trivial degenerate 4-qubit hybrid code.

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