Decoherence effects in the quantum qubit flip game using Markovian approximation

TL;DR

This paper investigates how decoherence affects the quantum penny flip game, showing that environmental noise disrupts equilibrium strategies and exploring control pulse optimization to improve players' success probabilities.

Contribution

It introduces a quantum penny flip game model incorporating Markovian decoherence channels and analyzes the impact on game strategies and equilibrium stability.

Findings

Decoherence destroys the Nash equilibrium of the Pauli strategy.

Optimized control pulses can increase winning probabilities under decoherence.

Different decoherence channels have distinct effects on game dynamics.

Abstract

We are considering a quantum version of the penny flip game, whose implementation is influenced by the environment that causes decoherence of the system. In order to model the decoherence we assume Markovian approximation of open quantum system dynamics. We focus our attention on the phase damping, amplitude damping and amplitude raising channels. Our results show that the Pauli strategy is no longer a Nash equilibrium under decoherence. We attempt to optimize the players' control pulses in the aforementioned setup to allow them to achieve higher probability of winning the game compared to the Pauli strategy.