Project: The relativistic-QFT chapter of the Bell-inequality problem
Target: IQOQI Open Quantum Problems #1 (Werner, All the Bell inequalities), #26 (Gill, Bell inequalities holding for all quantum states), #32 (Gisin, many questions, a few answers). Companion to long-range-bell-decay-project.
These problems are posed entirely in the finite-dimensional / correlation-polytope setting. Nobody has written the relativistic-QFT chapter, and the group owns that vocabulary. The aim is not to “solve” #1 in full but to plant a flag with a genuine, bounded result on type III₁ local algebras.
1. Thesis statement
Characterize which finite-dimensional Bell families (CHSH, CGLMP, Mermin) retain nontrivial content as constraints on type III local algebras, and prove the QFT counterpart of “Bell inequalities holding for all quantum states” (#26): that the Reeh–Schlieder property forbids any universal classical bound in a local region — inverting the finite-dimensional intuition.
2. Why it fits the group
Low marginal cost: shares the entire Weyl operator / modular toolkit and personnel with long-range-bell-decay-project. Direct extension of the group’s Mermin paper (Phys. Rev. D 109, 045020) and the bounded-Hermitian operator class (Phys. Rev. D 112).
3. Phased plan (~6–8 months, in the slipstream of Project 1)
Phase 1 — Translate (4–6 wks)
Lift the CGLMP and Mermin families into the Weyl-operator / modular setting, extending Phys. Rev. D 109, 045020.
Phase 2 — Prove the universality statement (4–6 wks)
The type III counterpart of #26, via Reeh–Schlieder + cyclicity of the vacuum: no local region admits a state-independent classical bound.
Phase 3 — Position paper (3–4 wks)
A single paper planting the flag across #1/26/27/32.
4. Targets & people
SciPost / PRD / Rev. Phys. Lead: Marcelo + silvio-paolo-sorella + itzhak-roditi; shares students with long-range-bell-decay-project.
5. Connection to existing wiki questions
- bell-chsh-in-holographic-setting — the type III characterization feeds the holographic boundary-algebra question
- higher-spin-bell-inequalities — the operator-class translation overlaps
6. Sequencing within the OQP program
Companion to the spine long-range-bell-decay-project; near-free because it reuses the same machinery. Independent of embezzlement-capacity-project.
Project plan committed 2026-06-19. Companion to long-range-bell-decay-project. Part of the bell-inequalities-qft line.