The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs

As the paper states it, in briefMinimizing Petz–Rényi information radii over classical–quantum channels compatible with a graph gives a continuum of points between known graph parameters; a 1440-vertex graph has $\mathrm{\Sigma }(G)$ strictly below the projective rank of its complement.

• Answered Do the middle links of the Duan–Winter chain of zero-error quantities ever separate, and what are they on the pentagon? posed by others
• Answered Is the Lovász number the only Rényi point in the entanglement-assisted spectrum of graphs?
• Open Is the projective rank of a graph’s complement in its entanglement-assisted spectrum? left open

Machine checks

Deterministic checks with pinned output, including an exact re-check of Theorem D. Version 1.1.0 corrected an overstated claim of version 1.0.0. Corrections

Lean

None.

Peer review

Not yet.

Every check here is internal. How we check results.

Novelty

New, with named precedent: Vrana’s interpolation already gives a continuum with the same values on the pentagon in the ordinary asymptotic spectrum; the new points lie in the entanglement-assisted spectrum. The three endpoint quantities are Duan and Winter’s, and order zero is due to Schrijver (as credited by Dalai) and to Duan and Winter.

PDF

papers/lovasz-v1.2.1.pdf, version 1.2.1, 805,507 bytes.

SHA-256 477dd4d6a4142cc130e345cd496bcfa81035e389201fdfa46f5d5fc74c6aeb82

DOI

10.5281/zenodo.23375704; all versions 10.5281/zenodo.22983498

Code

github.com/Apsiape/the-lovasz-number-is-not-alone

arXiv

arXiv:2610.20775

1. 14 Oct 2026Version 1.2.1. Credit added to Oufkir, Yao and Berta for the data-processing inequality behind non-signalling simulation, and to Wang and Duan (2018); Shariat, Hoogsteder-Riera and Tomamichel are described as giving an alternative proof. Section 1.1 said “the first three” terms of the Duan–Winter chain are radii, which would have included S_NS; corrected. A verification section that printed a number matching no statement of the paper is removed.doi:10.5281/zenodo.23375704
2. 13 Oct 2026Version 1.1.1. Credit and precision, after an attribution audit and a referee audit that found no false result: θ₀ = θ is credited to Schrijver (as Dalai’s Theorem 8), to Duan and Winter, and to Cabello, Severini and Winter; Wang and Duan’s answer to Duan and Winter’s question, Vrana’s continuum on C₅ in the ordinary spectrum, Li and Zuiddam, and others are credited; a figure caption’s witness radius had been rounded in the unsafe direction. No theorem changes.doi:10.5281/zenodo.23328240
3. 30 Sep 2026Version 1.1.0. Version 1.0.0 stated that both pentagon geometries in Figure 4 are nonoptimal throughout 0 < α < 1/2; the displayed bounds do not show this. Version 1.1.0 states only the proved regimes. The package also corrects a SHA-256 digest in the certificate README.doi:10.5281/zenodo.23066485

All corrections, and what counts as one.

@misc{mghirbi2026lovasz,
  author        = {Mghirbi, Nidhal and Douglas, Seth},
  title         = {The {L}ovász number is not alone: a continuum of {R}ényi points in the entanglement-assisted spectrum of graphs},
  year          = {2026},
  version       = {1.2.1},
  doi           = {10.5281/zenodo.23375704},
  url           = {https://doi.org/10.5281/zenodo.23375704},
  eprint        = {2610.20775},
  archiveprefix = {arXiv}
}

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