Impure codes exceeding the pure bounds for quantum local recovery
Carlos Galindo, Fernando Hernando, Helena Mart\'in-Cruz, Ryutaroh Matsumoto
TL;DR
This paper introduces a family of impure quantum codes that surpass existing bounds for pure quantum locally recoverable codes, highlighting new possibilities in quantum error correction.
Contribution
The authors present a new family of impure CSS codes based on J-affine variety codes that exceed bounds applicable to pure quantum locally recoverable codes.
Findings
Impure codes can outperform pure codes in local recovery bounds.
A connection between bounds on quantum local recovery and weight-constrained stabilizer codes is discussed.
The paper provides explicit examples of codes exceeding traditional bounds.
Abstract
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 -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.
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