Entanglement-Assisted Quantum Codes from Cyclic Codes - INSPIRE

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Entanglement-Assisted Quantum Codes from Cyclic Codes

Francisco Revson F. Pereira
(
- Google Inc.
)
,
Stefano Mancini
(
- U. Camerino (main) and
- INFN, Perugia
)

Dec 24, 2022

12 pages

Published in:

Entropy 25 (2023) 1, 37

Published: Dec 24, 2022

DOI:

10.3390/e25010037

View in:

AMS MathSciNet

reference search13 citations

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Abstract: (MDPI)

Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer formalism. In this paper, we provide a general method to construct EAQEC codes from cyclic codes. Afterwards, the method is applied to Reed–Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of EAQEC codes. Three families have been created: two families of EAQEC codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound.

quantum codes
Reed–Solomon codes
BCH codes
maximal distance separable
maximal entanglement
entanglement
singleton
quantum error correction
stability
Euclidean

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Figures(0)

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