Quantum version of a generalized Monty Hall game and its possible applications to quantum secure communications

TL;DR

This paper introduces a quantum version of a generalized Monty Hall game with flexible parameters, analyzes player payoffs with different initial states, and explores applications in quantum secure communication protocols.

Contribution

It presents a novel quantum Monty Hall game framework with variable parameters and extends it to multi-player scenarios for quantum network applications.

Findings

Classical payoff is recovered under specific conditions.

Entangled initial states can alter the expected payoff.

The game mechanics can be applied to quantum key distribution protocols.

Abstract

In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected payoff of the player, using both a separable and an entangled initial-state. In the two cases, the classical mixed-strategy payoff is recovered under certain conditions. Lastly, we extend our quantum scheme to include multiple independent players, and use this extension to sketch two possible application of the game mechanics to quantum networks, specifically, two validated, mult-party, key-distribution, quantum protocols.