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Quantum locally recoverable code with intersecting recovery sets
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We introduce the concept of quantum locally recoverable codes (qLRCs) with intersecting recovery sets. We derive a singleton-like bound for these codes by leveraging the additional information provided by the intersecting recovery sets. Furthermore, we provide a construction for qLRCs with intersecting recovery sets by introducing a variation of the hypergraph product. Finally, we apply our qLRC methods to obtain improved results for classical LRCs. These results may provide new insights into the locality of quantum error correction code.
Forward citations
Cited by 4 Pith papers
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Entanglement-Assisted Quantum Locally Recoverable Codes: Characterizations, Bounds, and Constructions
First explicit optimal pure CSS-like EAQLRC families are constructed from ℓ-intersection MDS pairs and block parity-check matrices, with Singleton-like optimality and nontrivial locality.
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CSS Quantum LRCs with Intersecting Recovery Sets: Constructions and Bounds
CSS quantum locally recoverable codes with intersecting recovery sets are characterized by classical codes with common recovery sets, and explicit binary families with high rates are constructed.
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Entanglement-Assisted Quantum Locally Recoverable Codes: Bounds, Optimal Constructions, and Achievability
Entanglement-assisted quantum locally recoverable codes can be constructed from arbitrary classical LRC pairs, and this paper proves bounds, optimality conditions, and explicit constructions for them.
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Information locality of a quantum locally recoverable code
For quantum codes built from finite-field linear codes, a more accurate locality measure and an algorithm reduce the number of qudits and measurements needed for erasure repair.
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