Quantum

Asymmetric Entanglement-Assisted Quantum Locally Recoverable Codes

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Briefings

This research introduces entanglement-assisted quantum locally recoverable codes (EA-qLRCs) with asymmetric locality parameters {r_X, r_Z}, addressing the physical asymmetry between bit-flip and phase-flip errors. The study derives bounds for these codes and characterizes when they achieve the Singleton bound, providing a framework for fault-tolerant quantum memories. The findings are presented as a preprint on arXiv:2610.23889v1.

Key points

• The study introduces EA-qLRCs with asymmetric locality {r_X, r_Z}, correcting X-type errors from r_X+1 and Z-type errors from r_Z+1 coordinates.
• A sufficient condition for asymmetric locality is extended to the CSS framework, enabling derivation of Singleton, Griesmer, and Plotkin bounds for AEA-qLRCs.

Context

Quantum memories require fault-tolerant storage, yet physical noise is rarely symmetric between bit-flip and phase-flip errors. Existing qLRCs use a single locality parameter r, which is suboptimal for asymmetric noise. This work provides a new framework for asymmetric EA-qLRCs using separate classical code conditions.

Limitations

The evidence is a preprint (arXiv:2610.23889v1) with no experimental validation or physical implementation data. Bounds are theoretical and depend on classical code properties. Exact conditions for Singleton bound equality remain to be characterized.

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