Stabilizer Formalism for EAQECCs with Noise ebits
Ruihu Li, Guanmin Guo, Yang Liu, and Hao Song
TL;DR
This paper develops a stabilizer formalism for entanglement-assisted quantum error-correcting codes (EAQECCs) with noisy ebits, unifying existing schemes and enabling the construction and analysis of new codes.
Contribution
It introduces a novel stabilizer formalism for EAQECCs with noise ebits, connecting it to symplectic geometry and additive codes, and demonstrates its application in code construction.
Findings
Unified formalism for EAQECCs with noisy ebits
Construction of new EAQECCs with performance analysis
Inclusion of existing schemes as special cases
Abstract
We introduce a stabilizer formalism for EAQECCs with noise ebits, using special subgroups of product groups of two Pauli groups. This formalism includes the two coding schemes,given by Lai and Brun (C.Y. Lai and T. A. Brun, PHYSICAL REVIEW A 86, 032319 (2012)), for EAQECCs with imperfect ebits as special cases. Then two equivalent formalisms of the formalism are derived in nomenclature of sympletic geometry and additive codes. We apply this theory to construct some EAQECCs with noise ebits, and analyze their performance.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Wireless Communication Techniques · Digital Filter Design and Implementation