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

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.

This is a continuation of arXiv:2608.04403

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2609.23316 [quant-ph]

(or arXiv:2609.23316v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23316 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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