Three-player quantum Kolkata restaurant problem under decoherence

TL;DR

This paper investigates how various quantum decoherence channels affect the payoffs and equilibrium in a three-player quantum Kolkata restaurant problem using tripartite entangled qutrit states.

Contribution

It analyzes the impact of different decoherence channels on players' payoffs and shows that the Nash equilibrium remains unchanged under decoherence effects.

Findings

Alice's payoff is heavily influenced by amplitude damping noise.

Depolarizing noise becomes dominant at high decoherence levels.

Nash equilibrium remains stable despite decoherence.

Abstract

Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice's payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice's payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50 % decoherence. It is also seen that for maximum decoherence (p=1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice's payoff. Therefore, the problem becomes noiseless one at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.