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Quantum Machine Learning Quantum Simulation Entanglement Theory Quantum Correlations

The NPA hierarchy does not always attain the commuting operator value

arXiv
Authors: Marco Fanizza, Larissa Kroell, Arthur Mehta, Connor Paddock, Denis Rochette, William Slofstra, Yuming Zhao

Year

2025

Paper ID

51788

Status

Preprint

Abstract Read

~2 min

Abstract Words

89

Citations

N/A

Abstract

We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. Specifically, there is a computable mapping from Turing machines to /boolean constraint system (BCS) nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. As a corollary, there is a BCS game for which the value of the Navascués-Pironio-Acín (NPA) hierarchy does not attain the commuting operator value at any finite level.

Why This Paper Matters

  • This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
  • It adds a 2025 reference point for readers tracking recent quantum research.
  • We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2510.04943 [2] arXiv https://arxiv.org/abs/2510.04943 [3] Publisher https://arxiv.org/abs/2510.04943

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