Post-selection games

Víctor Calleja Rodríguez; Ivan A. Bocanegra-Garay; Mateus Araújo

doi:10.22331/q-2026-11-05-2259

Post-selection games

Víctor Calleja Rodríguez¹, Ivan A. Bocanegra-Garay¹, and Mateus Araújo^1,2

¹Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain
²Laboratory for Disruptive Interdisciplinary Science (LaDIS), Universidad de Valladolid, 47011 Valladolid, Spain.

Published:	2026-11-05, volume 10, page 2259
Editor:	Ravi Kunjwal
Eprint:	arXiv:2601.18861v3
Doi:	https://doi.org/10.22331/q-2026-11-05-2259
Citation:	Quantum 10, 2259 (2026).

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Abstract

In this paper, we introduce post-selection games, a generalization of nonlocal games where each round can be not only won or lost by the players, but also discarded by the referee. Such games naturally formalize possibilistic proofs of nonlocality, such as Hardy's paradox. We develop algorithms for computing the local and Tsirelson bounds of post-selection games. Furthermore, we show that they have an unbounded advantage in statistical power over traditional nonlocal games, making them ideally suited for analysing Bell tests with low detection efficiency.

Featured image: Statistical power of the CHSH nonlocal game and the Hardy post-selection game as a function of detection efficiency.

Popular summary

Quantum nonlocality can be demonstrated via the use of nonlocal games: cooperative games where a referee sends questions to distant players that try to coordinate their answers without communicating. Their key feature is that players using entanglement can win the game with higher probability than those limited by classical strategies. In order to estimate this probability the game is played over many rounds, where in each round the referee decides whether the answers satisfy or not the question.

Experimental demonstrations of nonlocality are challenging because of its high sensitivity to noise, that tends to drown out the quantum signal. The noise is not uniform, though, as some answers are more affected than others. In order to go around that, we generalize nonlocal games to post-selection games, where the referee can not only accept or reject the answers, but also entirely discard a round. The players can then use this freedom to make the noisier answers be discarded. As the resulting data is much cleaner, we need much less of it to have conclusive statistics.

► BibTeX data

@article{CallejaRodriguez2026postselectiongames,
  doi = {10.22331/q-2026-11-05-2259},
  url = {https://doi.org/10.22331/q-2026-11-05-2259},
  title = {Post-selection games},
  author = {Calleja Rodr{\'{i}}guez, V{\'{i}}ctor and Bocanegra-Garay, Ivan A. and Ara{\'{u}}jo, Mateus},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2259},
  month = nov,
  year = {2026}
}

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