Quantum Synchronizable Codes on Sextic Cyclotomy
This work addresses synchronization issues in quantum communication, but it appears incremental as it builds on existing CSS code frameworks with specific cyclic codes.
The paper tackled the problem of constructing quantum synchronizable codes that correct both quantum noise and block misalignment, achieving synchronization capabilities at the upper bound and good error-correcting performance using cyclic codes from sextic cyclotomy.
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes constructed are CSS quantum error-correcting codes whose synchronization capabilities reach the upper bound. And we use cyclic codes gained by sextic cyclotomic classes to construct two classes of quantum synchronizable codes. Moreover, the quantum synchronizable codes are posses good error-correcting capability towards bit error and phase error, since the cyclic codes we used are optimal or almost optimal.