Nonlocal games, compression theorems, and the arithmetical hierarchy

@article{Mousavi2022NonlocalGC,
  title={Nonlocal games, compression theorems, and the arithmetical hierarchy},
  author={Hamoon Mousavi and Seyed Sajjad Nezhadi and Henry S. Yuen},
  journal={Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing},
  year={2022}
}
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 1/2 is complete for the class Σ1 (i.e., ). A result of Slofstra implies that deciding whether the commuting operator value of a nonlocal… 

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