Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations
Source: Originally published on arXiv quant-ph on August 4, 2026.
arXiv:2608.00124v1 Announce Type: new 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 o...
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