The Quantum Monty Hall Problem

TL;DR

This paper explores a quantum adaptation of the Monty Hall problem, demonstrating that quantum strategies, especially entanglement, can influence the game's outcome and optimal strategies.

Contribution

It introduces a quantum version of the Monty Hall problem and analyzes how quantum information storage affects the game’s strategies and outcomes.

Findings

Quantum strategies outperform classical ones for the player.

Entanglement enables the quiz master to optimize information encoding.

Quantum information storage can alter the game's value and strategies.

Abstract

We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.