Quantum Monty Hall problem under decoherence

TL;DR

This paper investigates how different types of quantum decoherence affect the outcomes and strategies in the quantum Monty Hall problem, revealing that certain noise channels alter the game's equilibrium and payoffs.

Contribution

It provides a detailed analysis of the impact of amplitude damping, depolarizing, and dephasing channels on the quantum Monty Hall game, highlighting how decoherence influences strategic stability and payoffs.

Findings

Depolarizing channel creates a Nash equilibrium for Alice's quantum strategy.

Dephasing noise does not affect the quantum Monty Hall game.

Amplitude damping leads to symmetrical Bob's payoffs with a maximum at p=0.5.

Abstract

We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice's quantum strategy. Where as in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, the Bob's payoffs are found symmetrical with maximum at p=0.5 against his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strategy remains always dominant against any choice of Alice's strategy.