The Quantum Locker Puzzle

TL;DR

This paper demonstrates that quantum strategies can dramatically outperform classical ones in the locker puzzle, achieving perfect success where classical strategies fail, even under stricter game rules.

Contribution

It introduces quantum strategies that enable perfect success in the locker puzzle, surpassing classical probability limits and analyzing variants with stricter rules and cheating referees.

Findings

Quantum players succeed with probability 1.

Classical players' success probability approaches zero under stricter rules.

Quantum advantage persists even with a cheating referee.

Abstract

The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot succeed with probability greater than 1-ln2 \approx 0.31, no matter how many players are involved. Our contribution is to show that quantum players can do much better--they can succeed with probability 1. By making the rules of the game significantly stricter, we show a scenario where the quantum players still succeed perfectly, while the classical players win with vanishing probability. Other variants of the locker puzzle are considered, as well as a cheating referee.