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<p>Existing literature provides several bounds for quantum local recovery, which essentially consider the number of message qudits, the distance, the length, and the locality of the involved codes. We give a family of <i>J</i>-affine variety codes that result in impure CSS codes. These quantum codes exceed several of the above mentioned bounds that apply to pure quantum locally recoverable codes. We also discuss a connection between bounds on quantum local recovery and on weight-constrained stabilizer codes.</p>

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Impure codes exceeding the pure bounds for quantum local recovery

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月3日

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  • Carlos Galindo,
  • Fernando Hernando,
  • Helena Martín-Cruz,
  • Ryutaroh Matsumoto

摘要

Existing literature provides several bounds for quantum local recovery, which essentially consider the number of message qudits, the distance, the length, and the locality of the involved codes. We give a family of J-affine variety codes that result in impure CSS codes. These quantum codes exceed several of the above mentioned bounds that apply to pure quantum locally recoverable codes. We also discuss a connection between bounds on quantum local recovery and on weight-constrained stabilizer codes.