bibkey: knilllaflamme1997correction authors: E. Knill and R. Laflamme year: 1997 title: Theory of quantum error-correcting codes doi: 10.1103/PhysRevA.55.900 claim: A quantum code corrects a specified finite error family exactly when the compressed pairwise error products are scalar on the code. strata_touched:

• D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding license: citation-only triage: anchor

Exact correction and orthogonal syndromes

The error-product criterion and syndrome recovery are established quantum error-correction results. The theory supplement supplies the construction for the fixed finite input space and public-result conventions it uses. Neither the old theorem nor the finite candidate Lean identities independently establish a physical string model or a spacetime metric.

For a fixed code, detecting every operator supported on fewer than the code distance gives scalar compressions of those operators. Applied to an exactly invariant code under a specified GKLS generator, this bounds the small-support jump terms; it does not address active correction, moving code spaces, or evolutions that leave the code temporarily. This use of the criterion is not a gravitational or spacetime statement.

Source: https://doi.org/10.1103/PhysRevA.55.900

Verified locator

• DOI: https://doi.org/10.1103/PhysRevA.55.900 resolves to the Physical Review A article titled above.
• The cited result is the exact scalar error-product criterion for a specified code and error family. The present finite decoding identity is proved in the repository and does not import a physical spacetime model.