Pith. sign in

REVIEW 2 cited by

A simple approach to approximate quantum error correction based on the transpose channel

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 0909.0931 v2 pith:SNCINQP2 submitted 2009-09-04 quant-ph

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

We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions, and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement.

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. Connecting Quantum Tomography and Quantum Retrodiction

    quant-ph 2026-06 unverdicted novelty 5.0 of 10

    The Petz recovery map equals the gradient of the log-likelihood in maximum-likelihood tomography, unifying retrodiction and state reconstruction via a shared iterative procedure.

Pith tools