Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations

Quantum Physics arXiv:2608.00124 (quant-ph) [Submitted on 31 Jul 2026] Title:Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations Authors:Aaron Alai View a PDF of the paper titled Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations, by Aaron Alai View PDF HTML (experimental) Abstract:Bell derivations rest on locality, determinism, and measurement independence. Hall [Phys. Rev. Lett. 105, 250404 (2010)] priced the third assumption exactly for the singlet state, and in the Kochen-Specker analysis of Phys. Rev. A 84, 022102 (2011) priced the four tripartite Mermin perfect correlators at a surrendered fraction of 1/3, leaving open the problem of an optimal model for the Mermin state itself. This paper solves the faithful version of that problem -- every full correlator reproduced and every proper-subset marginal vanishing -- and extends it to thirteen parties. A reduction theorem shows the faithfulness constraints are free, so Hall's correlator-only threshold is promoted to the faithful value, F(3) = 1/3; linear-programming optima, certified exactly by an integer-arithmetic squeeze between a proven lower bound and an explicit construction, then give F(5) = 2/5, F(7) = 4/9, F(9) = 8/17, F(11) = 16/33, and F(13) = 32/65, each value through n = 11 repeated at the following even size. All computed points obey the closed law F = R/[2(R+1)] with R = 2^floor((n-1)/2) the Mermin violation ratio, a proven combinatorial lower bound is tight on every computed core, and a universal ceiling F new | recent | 2026-08 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)