The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs
Year: 2026
Type: preprint
Abstract: Credit and precision fixes after a final pre-arXiv review. No theorem, bound, certificate value or numbering changes. Credit. That non-signalling-assisted simulation cannot increase the Rényi capacity of a classical channel follows from the data-processing inequality for channel divergences under non-signalling maps of Oufkir, Yao and Berta (Ann. Henri Poincaré 2026, Lemma 24; Lemma 25 in arXiv:2509.15200v1). Related work now credits them, and describes Shariat, Hoogsteder-Riera and Tomamichel as giving an alternative proof, as their v2 does. Section 1.1. The sentence introducing the radii now names the three terms of the Duan–Winter chain that are radii (log2 theta, C_min, log2 Sigma); version 1.2.0 said "the first three", which would have included S_NS. C_min and Sigma are defined as infima, without the shorthand "real SDP simulation value". Abstract. The three quantities are the smallest information radii of compatible channels; the main step is stated for channels that need not factor; the last sentence states the direction of Theorem D (Sigma(G) <= xi_f(complement of G), strict on a 1440-vertex graph). The abstract is shortened to 1910 characters after expanding the paper's macros, within arXiv's limit. Introduction. "Seed" is no longer used before Section 6 defines it; a clause after Theorem D notes that it rules out every member of the family, since theta_alpha <= Sigma for alpha <= 2; a caveat repeated in Related work is removed. Open problems. "Non-commutative graphs" cites Wang and Duan (IEEE Trans. Inf. Theory 64 (2018)): there the entanglement-assisted capacity can be strictly below the quantum Lovász number, so that spectrum has another point (Li and Zuiddam, remark after Theorem 33). Precision. Figure 4 caption (the claim is for the umbrella vectors); "at least as strong" for the flat bound in Section 7.1; Appendix A names the key of Tr sigma; C_min is an infimum. References. Oufkir, Yao and Berta, and Wang and Duan (2018) added; Oufkir, Tomamichel and Berta updated to Lett. Math. Phys. 116 (2026), article 33; Ji's entry prints its arXiv number. Build. \pdfoutput=1 heads main.tex, for arXiv. Verification. Section [2] of verify/entanglement_assisted_spectrum.py printed a difference of two hard-coded rationals that matched no statement of the paper; it is removed, and the section keeps the exact pentagon endpoint check. Theorem C is checked by verify/small_graph_separation.py, as before. In the pinned output the section header changes and the L - R line is gone.
Source: arXiv (Cornell University)
Authors: Mghirbi, Nidhal, Douglas, Seth
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214467176