Geometry of symplectic group and optimal EAQECC codes

• URL: http://arxiv.org/abs/2501.15465v1
• Date: Sun, 26 Jan 2025 09:58:20 GMT
• Title: Geometry of symplectic group and optimal EAQECC codes
• Authors: Ruihu Li, Yuezhen Ren, Chaofeng Guan, Yang Liu,
• Abstract summary: A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented.
• Score: 4.992350404374237
• License:
• Abstract: A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented. Relations of symplectic subspaces and quaternary additive codes concerning parameters of EAQECCs are described. Thus, parameters of EA stabilizer codes are revealed in the nomenclature of additive codes. Our techniques enable us solve some open problems about optimal EAQECCs and entanglement-assisted quantum minimum distance separable (EAQMDS) codes, and are also useful for designing encoding and decoding quantum circuit of EA stabilizer codes.

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