A unification of the coding theory and OAQEC perspectives on hybrid codes. (English) Zbl 1531.81071
Summary: 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.
MSC:
| 81P70 | Quantum coding (general) |
| 94A60 | Cryptography |
| 65B05 | Extrapolation to the limit, deferred corrections |
| 81P73 | Computational stability and error-correcting codes for quantum computation and communication processing |
| 81P47 | Quantum channels, fidelity |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
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