Quantum

The Lov\'asz number is not alone: a continuum of R\'enyi points in the entanglement-assisted spectrum of graphs

Read full article at source ↗

Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 16/10/2026, 04:13:24 UTC.

Briefings

A new study by Li and Zuiddam reveals a continuum of R\'enyi points in the entanglement-assisted spectrum of graphs, extending beyond the previously known Lov\'asz number. The research identifies three quantities—Duan and Winter's log of the Lov\'asz number, the minimal Holevo capacity, and the no-signalling simulation cost—as the smallest information radii for classical-quantum channels. These quantities form a family parameterized by alpha between 0 and 2, with the family's members lying within the spectrum. The study provides exact proofs for the pentagon's range, certifies a conjecture on the minimal Holevo capacity, and establishes that the no-signalling simulation rate equals its single-letter value. It also proves a conjecture on the 32-vertex magic square graph and establishes a rank inequality for the complement of a 1440-vertex graph.

Key points

• Li and Zuiddam's entanglement-assisted asymptotic spectrum of graphs consists of normalized graph parameters additive under disjoint unions and multiplicative under strong products.
• The Lov\'asz number was the only known element in this spectrum until this study, which found a continuum of others.

Context

This research addresses the long-standing question of whether the Lov\'asz number is the sole element in the entanglement-assisted spectrum of graphs, as proposed by Li and Zuiddam. The findings provide a complete characterization of the spectrum using R\'enyi divergences of orders 0, 1, and 2, and extend this to sandwiched R\'enyi radii.

Limitations

The study relies on arXiv preprint data and does not include peer-reviewed publication details. Results are subject to verification as the source is untrusted. Specific numerical values and proofs are presented as established facts within the context of the preprint.

Generated by Bittrees-hosted qwen35-2b sha256:aaf42c8b7c3c on 16/10/2026, 05:04:31 UTC. Based on publisher-provided feed evidence; may not cover the full original article. Check the source for details.

View archived briefing on IPFS
bafybeiddluqgxigr6g5bqzcjnzferxrqzfuuzao2wp5pvcmgg7yc4deu6q