• Corpus ID: 238583136

Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy

@article{Mousavi2021NonlocalGC,
  title={Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy},
  author={Hamoon Mousavi and Seyed Sajjad Nezhadi and Henry S. Yuen},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.04651}
}
We investigate the connection between the complexity of nonlocal games and the arithmetical hierarchy, a classification of languages according to the complexity of arithmetical formulas defining them. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that deciding whether the (finite-dimensional) quantum value of a nonlocal game is $1$ or at most $\frac{1}{2}$ is complete for the class $\Sigma_1$ (i.e., $\mathsf{RE}$). A result of Slofstra implies that deciding whether the… 

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