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PreprintCC BY 4.0HAL

Bell nonlocality does not imply violation of nonlocal games

  • Ricardo Faleiro
  • Lucas Emanuel Antunes Porto
  • Marco Túlio Quintino
  • Flavien Hirsch
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Abstract

Nonlocal games offer a conceptually clear way to reason about Bell nonlocality. However, we show that as originally defined, and most commonly used, i.e. with a deterministic predicate, they cannot be complete witnesses of nonlocality. Concretely, we prove the existence of nonlocal behaviours which do not violate any such nonlocal game. Furthermore, we also show that quantum mechanics can produce these game-classical nonlocal behaviours. We prove that this phenomenon exists in every bipartite scenario $(X,Y,A,B)$ with X,Y≥2 and A,B≥4.

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Cite

BibTeXRIS
BibTeX
@misc{faleiro2026bell,
  title = {{Bell nonlocality does not imply violation of nonlocal games}},
  author = {Ricardo Faleiro and Lucas Emanuel Antunes Porto and Marco Túlio Quintino and Flavien Hirsch},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06799},
  eprint = {2610.06799},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05787551v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bell nonlocality does not imply violation of nonlocal games
AU  - Ricardo Faleiro
AU  - Lucas Emanuel Antunes Porto
AU  - Marco Túlio Quintino
AU  - Flavien Hirsch
PY  - 2026
DA  - 2026/10/05
PB  - HAL
DO  - 10.48550/arxiv.2610.06799
UR  - https://hal.science/hal-05787551v1
AB  - Nonlocal games offer a conceptually clear way to reason about Bell nonlocality. However, we show that as originally defined, and most commonly used, i.e. with a deterministic predicate, they cannot be complete witnesses of nonlocality. Concretely, we prove the existence of nonlocal behaviours which do not violate any such nonlocal game. Furthermore, we also show that quantum mechanics can produce these game-classical nonlocal behaviours. We prove that this phenomenon exists in every bipartite scenario $(X,Y,A,B)$ with X,Y≥2 and A,B≥4.
ER  -