We are a small research program that publishes preregistered computational studies. We are writing to invite independent replication of five related results about the Petz recovery map.
Each study first derived — analytically, before any computation — a specific number describing where the ordinary Petz map's recovery bound holds and where it fails on a fixed qubit witness, and then tested that number in a frozen, preregistered simulation campaign. All five tests reproduced the derived values. The numbers are concrete enough to be checked by anyone:
- a dephasing-dose onset at λ* = 0.8857288966 — the recovery gap is protected on a long initial interval and crosses zero exactly once, there;
- a recovery-deficit curve rising monotonically through 0, 0.545519, 1.023380, 1.389413, 1.534877 as the dephasing dose goes from 0 to 1;
- a depolarizing-dose restoration threshold at ε* = 0.02124281;
- a depolarizing-dose gap curve rising monotonically and gradedly, with total rise 0.292424;
- a disorder-ensemble profile: across 1,024 random draws at each of five disorder amplitudes, the fraction of bound violations is 1.0, 1.0, 1.0, 0.956055, 0.844727.
For each study, the preregistration, the frozen protocol, the code, and the complete result record are public on the Open Science Framework:
- Dephasing onset — https://osf.io/b8skx/ (DOI: 10.17605/OSF.IO/B8SKX)
- Recovery-deficit curve — https://osf.io/yrcnx/ (DOI: 10.17605/OSF.IO/YRCNX)
- Restoration threshold — https://osf.io/jrhua/ (DOI: 10.17605/OSF.IO/JRHUA)
- Gap curve — https://osf.io/r5y2g/ (DOI: 10.17605/OSF.IO/R5Y2G)
- Ensemble profile — https://osf.io/q8tmg/ (DOI: 10.17605/OSF.IO/Q8TMG)
A replication needs no contact with us and no permission: the records are self-contained. If you re-run or re-derive any of these numbers, we commit to recording the outcome and linking it from the study's record — whether it agrees with ours or not. Questions about methods are welcome at start@axiovexsystems.com.
— Axiovex Systems, research program
