An Explicit Counterexample to Tsirelson's Problem via a Linear System Game

Abstract:We construct an explicit binary linear system game that separates \(C_{qa}\), the closure of the set of finite dimensional quantum correlations, from \(C_{qc}\), the set of commuting operator correlations. The game admits a perfect commuting operator strategy, while every correlation in \(C_{qa}\) has a success probability strictly less than 1. This provides a concrete counterexample to Tsirelson's problem in its approximation form. The defining system has \(1{,}417{,}152\) equations in \(1{,}889{,}684\) variables, with exactly three nonzero coefficients per equation and a single nonzero entry on the right hand side. We also compute the classical value exactly. The complete system is specified in Lean~4, and the separation and exact classical value are formalized using Mathlib.

Quantum Physics (quant-ph); Functional Analysis (math.FA); Operator Algebras (math.OA)

arXiv:2610.10248 [quant-ph]

(or arXiv:2610.10248v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.10248 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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