Quantum recovery from finitely many sharp questions
In plain wordsIf finitely many sharp yes-or-no measurements can each be recovered approximately after a channel, the whole quantum input, correlations included, is recoverable with proportional error whenever the measurements pass a checkable averaging test; for some families the best factor is (log d)² in dimension d.
The result
As the paper states it, in briefWhen approximate recovery of finitely many sharp binary observables guarantees recovery of the entire quantum input, with matching fixed-gap minimax bounds.
Questionson the index
How this was checked
- Exact certificates
- An exact-byte manifest and a saved axiom certificate.
- Lean
- Partial, twelve declarations: calibrated projections implying finite-word stability. No numbered recovery theorem is fully formalized.
- Peer review
- Not yet.
Every check here is internal. How we check results.
Novelty and credit
- Novelty
- New, with named precedent: Renes’s complementary-observable recovery and Bény’s analysis of approximate observable error correction. New, in the paper’s words: a quantitative implication from calibrated sharp questions to full recovery.
Versionsone, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| 1.0.0 | 10.5281/zenodo.22779671 | PDF hosted here. |
Paper, code and links
papers/fqr-v1.0.0.pdf, version 1.0.0, 452,840 bytes.SHA-256 d6407e7f92c0ad315e56a9a896dfa6a7e3716b154bb3bd184cdfc7daeb48bea3
Corrections
None so far.
All corrections, and what counts as one.
Cite
@misc{douglas2026fqr,
author = {Douglas, Seth},
title = {Quantum recovery from finitely many sharp questions},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.22779671},
url = {https://doi.org/10.5281/zenodo.22779671}
}