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

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.

4 pages

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Cited by in corpus (2)

• Stabilizer Formalism for Operator Algebra Quantum Error Correction
• Scalable and fault-tolerant preparation of encoded k-uniform states