Closed mixed-apparatus compression of Schur channels: exact–approximate separation and scheduled delivery

As the paper states it, in briefA Schur channel of Gram rank $k$ on dimension $d$ is implemented to error $\epsilon$ by one fixed unitary with apparatus dimension $O({\epsilon }^{-2}(\sqrt{k}+\ln d))$.

Machine checks

Finite numerical controls and a package verifier.

Lean

Partial: a finite no-signalling theorem and six inventory lemmas. Concentration, entropy bounds, compression and the asymptotic separation are not formalized.

Peer review

Not yet.

Every check here is internal. How we check results.

Novelty

New, with named precedent: Terhal and coauthors gave the square-root rank scale and the qualitative obstruction for extreme channels, and Rybár and Ziman’s no-reset setting and entropy accounting are precedents. New, in the paper’s words: an approximate Schur construction approaching that scale, with explicit overheads.

PDF

papers/schur-v1.0.0.pdf, version 1.0.0, 491,138 bytes.

SHA-256 39f8016cb14033a7a8fd73adaec2fe4caf5bd24a11edb7d65c02b2650b89c2f5

DOI

10.5281/zenodo.22785669

Code

github.com/Apsiape/closed-schur-channel-compression

None so far.

All corrections, and what counts as one.

@misc{douglas2026schur,
  author  = {Douglas, Seth},
  title   = {Closed mixed-apparatus compression of {S}chur channels: exact–approximate separation and scheduled delivery},
  year    = {2026},
  version = {1.0.0},
  doi     = {10.5281/zenodo.22785669},
  url     = {https://doi.org/10.5281/zenodo.22785669}
}

schur.bibAll papers as BibTeX