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Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery

  • Ryutaroh Matsumoto
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Abstract

For a general entanglement-assisted or unassisted quantum error-correcting code, a set of erasures, and an associated repair group, we propose a linear algebraic procedure to compute a reduced set of observables and a reduced repair group of codeword qudits for correcting the given erasures. The procedure has cubic complexity in the repair group size and the computed set of observables has the smallest possible size for correcting the given erasures. We specialize the general procedure to quantum codes constructed from Euclidean and Hermitian orthogonality, and provide closed-form upper bounds on the size of reduced repair groups for those special cases. Based on these closed-form bounds, we propose quantum counterparts of the information locality of classical local recovery.

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Cite

BibTeXRIS
BibTeX
@misc{matsumoto2026simultaneous,
  title = {{Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery}},
  author = {Ryutaroh Matsumoto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23316},
  eprint = {2609.23316},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23316},
}
RIS
TY  - UNPB
TI  - Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery
AU  - Ryutaroh Matsumoto
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23316
UR  - https://arxiv.org/abs/2609.23316
AB  - For a general entanglement-assisted or unassisted quantum error-correcting code, a set of erasures, and an associated repair group, we propose a linear algebraic procedure to compute a reduced set of observables and a reduced repair group of codeword qudits for correcting the given erasures. The procedure has cubic complexity in the repair group size and the computed set of observables has the smallest possible size for correcting the given erasures. We specialize the general procedure to quantum codes constructed from Euclidean and Hermitian orthogonality, and provide closed-form upper bounds on the size of reduced repair groups for those special cases. Based on these closed-form bounds, we propose quantum counterparts of the information locality of classical local recovery.
ER  -