Environmental influences on Quantum Monty Hall problem

TL;DR

This paper explores how decoherence affects the quantum Monty Hall problem, revealing that decoherence alters strategies and winning probabilities, with different effects depending on the type of decoherence channel.

Contribution

It introduces a reformulation of the quantum Monty Hall problem incorporating decoherence, identifying new Nash equilibria and strategy shifts caused by environmental effects.

Findings

Decoherence destroys the fairness of the quantum game.

Bob's winning probability exceeds 75% under amplitude damping without switching.

Different decoherence channels have distinct impacts on Bob's optimal strategy.

Abstract

We reformulate the quantum Monty Hall problem in the presence of decoherence. The decoherence destroys the fairness of the game. A new Nash equilibrium for a particular strategy profile in the presence of decoherence emerges. It is shown that in the presence of decoherence under the action of amplitude damping channel, Bob's winning probability is always higher than three-forth, irrespective of Alice's strategy, if he does not switch to the other door and always wins for a fully decohered case of the channel. Depolarizing channel damps up Bob's winning probability and gets better off if he sticks to his current selection. Phase damping channel leaves the winning probability unaffected. Unlike the classical and the quantum forms of the game, Bob's dominant strategy in the presence of decoherence is not switching.