Pith. sign in

REVIEW 2 cited by

General conditions for approximate quantum error correction and near-optimal recovery channels

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0907.5391 v4 pith:IVK5EXY3 submitted 2009-07-30 quant-ph

classification quant-ph
keywords recoverycodesconditionserrorfidelityapproximatechannelscorrection
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case entanglement fidelity of the overall process. We show that the optimal recovery fidelity can be predicted exactly from a dual optimization problem on the environment causing the noise. We use this result to obtain an easy-to-calculate estimate of the optimal recovery fidelity as well as a way of constructing a class of near-optimal recovery channels that work within twice the minimal error. In addition to standard subspace codes, our results hold for subsystem codes and hybrid quantum-classical codes.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Approximate Quantum Error Correction at Chiral Topological Edges

    quant-ph 2026-08 conditional novelty 7.0 of 10

    Chiral edge codes have local-erasure robustness governed by power-law exponents with hierarchy γ≥α≥min{α,β}, so the 2D code is at least as robust as its 1D CFT reduction.

  2. Certified boundary-magic witness for state-dependent proto-area in a holographic code

    hep-th 2026-07 conditional novelty 5.5 of 10

    Only matter-controlled bond motion yields state-dependent proto-area in a four-qubit holographic code, and a projected stabilizer-Rényi quadratic witness certifies it while total magic does not.

Pith tools