bibkey: barnumknill2002reversal
authors: H. Barnum and E. Knill
year: 2002
title: Reversing quantum dynamics with near-optimal quantum and classical fidelity
doi: 10.1063/1.1459754
claim: A reference-state transpose recovery construction attains near-optimal quantum and classical fidelity under the source theorem's conditions.
strata_touched:
  - D5/S3/Quantum/Recovery/SpectralTransposeRecovery
  - D5/S3/Quantum/Recovery/SpectralRecoveryCorrectness
license: citation-only
triage: anchor

Transpose-channel recovery

The source constructs a reversal adapted to a reference state and noise channel, with near-optimal entanglement/classical fidelity bounds. The maximally mixed logical reference specializes to the inverse-square-root support construction used in the current finite recovery theorem. The current text gives its exact-error-correction proof directly and does not import an unproved diamond-norm approximation rate from this fidelity theorem.

Source: https://arxiv.org/abs/quant-ph/0004088

The arXiv record reports revision v2 on 18 January 2026. Its authors state that the revision corrects an error in the proof of the main theorem that obstructed extension to ensembles containing more than one density matrix. The abstract/version note was checked; this note does not assert a line-by-line verification of the revised general approximate-fidelity proof. The repository’s exact finite recovery construction is proved directly from the scalar Kraus-product condition and does not rely on that general ensemble theorem.

Version-specific record: https://arxiv.org/abs/quant-ph/0004088v2

Verified locator

• DOI: https://doi.org/10.1063/1.1459754 resolves to the Journal of Mathematical Physics article titled above. The publisher page returned HTTP 403 here.
• Version-specific preprint: https://arxiv.org/abs/quant-ph/0004088v2 .
• The citation locates the reference-state reversal construction and its published fidelity result. The corrected general proof is not a premise of the repository’s exact finite recovery theorem.