Quantum PBR Theorem as a Monty Hall Game

TL;DR

This paper reformulates the quantum PBR theorem as a Monty Hall game, revealing how the nature of the quantum state influences winning probabilities and applying these ideas to enhance quantum teleportation reliability.

Contribution

It introduces a novel game-theoretic reformulation of the PBR theorem and explores implications for quantum teleportation.

Findings

Switching doors affects winning probabilities depending on the quantum state model.

In some cases, switching offers no advantage in the game.

Applying the concept improves quantum teleportation reliability.

Abstract

The quantum Pusey--Barrett--Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a $\psi$-ontic model (system's physical state) or to a $\psi$-epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a $\psi$-ontic or $\psi$-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability.