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  "path": "/abs/2602.09290v1",
  "publishedAt": "2026-02-11T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Yang P. Liu",
    "Shachar Lovett",
    "Kunal Mittal"
  ],
  "textContent": "**Authors:** Yang P. Liu, Shachar Lovett, Kunal Mittal\n\nWe prove that for any 3-player game $\\mathcal G$, whose query distribution has the same support as the GHZ game (i.e., all $x,y,z\\in \\\\{0,1\\\\}$ satisfying $x+y+z=0\\pmod{2}$), the value of the $n$-fold parallel repetition of $\\mathcal G$ decays exponentially fast: \\\\[ \\text{val}(\\mathcal G^{\\otimes n}) \\leq \\exp(-n^c)\\\\] for all sufficiently large $n$, where $c>0$ is an absolute constant. We also prove a concentration bound for the parallel repetition of the GHZ game: For any constant $ε>0$, the probability that the players win at least a $\\left(\\frac{3}{4}+ε\\right)$ fraction of the $n$ coordinates is at most $\\exp(-n^c)$, where $c=c(ε)>0$ is a constant. In both settings, our work exponentially improves upon the previous best known bounds which were only polynomially small, i.e., of the order $n^{-Ω(1)}$. Our key technical tool is the notion of \\emph{algebraic spreadness} adapted from the breakthrough work of Kelley and Meka (FOCS '23) on sets free of 3-term progressions.",
  "title": "Improved Parallel Repetition for GHZ-Supported Games via Spreadness"
}