Factorizable rational quantum channels at an explicit distance from finite tracial baths
In plain wordsAn explicit twelve-qubit quantum channel with simple rational entries can be run by a maximally mixed environment of infinite size, yet stays an explicit positive distance, though a tiny one, from every channel that finite maximally mixed environments run or approach.
The result
As the paper states it, in briefExplicit rational channels that are factorizable but not limits of channels implementable with a finite maximally mixed environment, at a positive and explicit distance from that closure.
Questionson the index
How this was checked
- Exact certificates
- Standard-library checks of the payload, the constants and the certificates, listed in Section 8 of the paper.
- Lean
- None.
- Peer review
- Not yet.
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Novelty and credit
- Novelty
- Extends named prior work: version 1.0 of this work and Haagerup and Musat’s criterion for Schur channels; the characteristic-five certificate runs Wang and Zhi’s method. New, in the paper’s words: the compiler, the leakage theorem without letter singletons, and the root certificate.
Versionstwo, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| 2.0.0 | 10.5281/zenodo.23196593 | PDF hosted here. | |
| 1.0.0 | 10.5281/zenodo.23093839 | Titled “A rational quantum channel beyond finite tracial baths”. |
Paper, code and links
papers/rational-channels-v2.0.0.pdf, version 2.0.0, 554,621 bytes.SHA-256 54decc274ca2b515e3c376aa42c47d68920b01b1d97ef323a189dd46ccb8b73c
- DOI
10.5281/zenodo.23196593; all versions 10.5281/zenodo.23093838
Corrections
None so far.
All corrections, and what counts as one.
Cite
@misc{mghirbi2026rationalchannels,
author = {Mghirbi, Nidhal and Douglas, Seth},
title = {Factorizable rational quantum channels at an explicit distance from finite tracial baths},
year = {2026},
version = {2.0.0},
doi = {10.5281/zenodo.23196593},
url = {https://doi.org/10.5281/zenodo.23196593}
}