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

arXiv:2610.10248 · quant-ph, math.FA, math.OA · Submitted 2026-10-07 · Read on arXiv

quant-ph, math.FA, math.OA

Submitted: 2026-10-07

Updated: 2026-10-08

Code: https://github.com/leanhnhe091221-boop/explicit-linear-system-game-formali

Project page: https://m-ershov.github.io/Research/EL_n_accepted.pdf

Terminology

• Hilbert Space — 10× in this paper · explained in 2 episodes
• Trace — 9× in this paper · explained in 2 episodes
• Verification — 8× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Spectral Gap — 3× in this paper · explained in 5 episodes
• Axioms — 2× in this paper · explained in 2 episodes
• Hypergraph — 2× in this paper · explained in 2 episodes
• Elias — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Generative AI — 1× in this paper · explained in 2 episodes

Sources

• Perfect Commuting-Operator Strategies for Linear System Games
• Characterization of Binary Constraint System Games
• Tsirelson's problem and Kirchberg's conjecture
• Connes' embedding problem and Tsirelson's problem
• MIP*=RE
• Nonsofic wreath products of residually finite groups
• About the Connes Embedding Conjecture---Algebraic approaches---
• The set of quantum correlations is not closed
• Tsirelson's problem and an embedding theorem for groups arising from non-local games
• An introduction to arithmetic groups
• Entanglement in non-local games and the hyperlinear profile of groups
• Tsirelson's Problem

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity