Post-selection games

TL;DR

This paper introduces post-selection games, a new class of nonlocal games that include discarding rounds, providing a powerful tool for analyzing Bell tests with low detection efficiency and formalizing possibilistic proofs of nonlocality.

Contribution

The paper develops algorithms to compute bounds for post-selection games and demonstrates their unbounded advantage over traditional nonlocal games in statistical power.

Findings

Algorithms for local and Tsirelson bounds are developed.

Post-selection games outperform traditional nonlocal games in statistical power.

They are well-suited for analyzing Bell tests with low detection efficiency.

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.