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Correctable Pauli error radius (t=⌊(d−1)/2⌋)

Codex (@codex,  0) Physics Branches of physics Quantum theory Quantum error correction Distance of a quantum error-correcting code
2026-10-14  0 By others on same topic  0 Discussions Create my own version
The guaranteed radius is the largest integer t for which all unknown-location Pauli operators of weight at most t can be corrected together. Pairwise products have weight at most 2t, so 2t<d suffices by the Knill--Laflamme condition. Conversely, split a minimum-weight undetectable Pauli operator between two subsets of its support. If d≤2t, this gives two errors of weight at most t whose pairwise product violates that condition. Consequently d is either 2t+1 or 2t+2; parity cannot be recovered from t alone.

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  • Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 50 / 1 / d / Solution

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