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Asymmetric Entanglement-Assisted Quantum Locally Recoverable Codes

  • Vijay Kumar
  • Ramakrishna Bandi
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Abstract

Locally recoverable codes (LRCs) permit reconstruction of a lost coordinate from a small subset of the remaining coordinates, a property that is a fundamental coding technique for distributed storage and, more recently, for fault-tolerant quantum memories and distributed storage systems. Existing constructions of quantum locally recoverable codes (qLRCs) and their entanglement-assisted generalizations (EA-qLRCs) impose a single locality parameter r governing recovery from both bit-flip (X-type) and phase-flip (Z-type) errors, even though physical noise is rarely symmetric between the two. We introduce entanglement-assisted quantum locally recoverable codes (EA-qLRC) with \emph{asymmetric locality} {rX,rZ}, in which X-type and Z-type errors are corrected from recovery sets of size at most rX+1 and rZ+1, respectively. We extend a stabilizer sufficient condition for this property and, in particular, the CSS framework, where asymmetric locality corresponds to separate locality conditions on the two classical codes π’ž1 and π’ž2 underlying the construction. From this characterization we derive Singleton-, Griesmer-, Plotkin-, sphere-packing-, and Cadambe\textendash Mazumdar-like bounds for CSS-type asymmetric EA-qLRCs (AEA-qLRCs) built from Proposition~\ref{CSS-EA-qLRC-Asym}, and we characterize exactly when a pure CSS-type AEA-qLRC built from a pair of classical LRCs attains the Singleton-like bound with equality.

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Cite

BibTeXRIS
BibTeX
@misc{kumar2026asymmetric,
  title = {{Asymmetric Entanglement-Assisted Quantum Locally Recoverable Codes}},
  author = {Vijay Kumar and Ramakrishna Bandi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23889},
  eprint = {2610.23889},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23889},
}
RIS
TY  - UNPB
TI  - Asymmetric Entanglement-Assisted Quantum Locally Recoverable Codes
AU  - Vijay Kumar
AU  - Ramakrishna Bandi
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.23889
UR  - https://arxiv.org/abs/2610.23889
AB  - Locally recoverable codes (LRCs) permit reconstruction of a lost coordinate from a small subset of the remaining coordinates, a property that is a fundamental coding technique for distributed storage and, more recently, for fault-tolerant quantum memories and distributed storage systems. Existing constructions of quantum locally recoverable codes (qLRCs) and their entanglement-assisted generalizations (EA-qLRCs) impose a single locality parameter r governing recovery from both bit-flip (X-type) and phase-flip (Z-type) errors, even though physical noise is rarely symmetric between the two. We introduce entanglement-assisted quantum locally recoverable codes (EA-qLRC) with \emph{asymmetric locality} {r_X,r_Z}, in which X-type and Z-type errors are corrected from recovery sets of size at most r_X+1 and r_Z+1, respectively. We extend a stabilizer sufficient condition for this property and, in particular, the CSS framework, where asymmetric locality corresponds to separate locality conditions on the two classical codes π’ž_1 and π’ž_2 underlying the construction. From this characterization we derive Singleton-, Griesmer-, Plotkin-, sphere-packing-, and Cadambe\textendash Mazumdar-like bounds for CSS-type asymmetric EA-qLRCs (AEA-qLRCs) built from Proposition~\ref{CSS-EA-qLRC-Asym}, and we characterize exactly when a pure CSS-type AEA-qLRC built from a pair of classical LRCs attains the Singleton-like bound with equality.
ER  -