Qubit flip game on a Heisenberg spin chain

TL;DR

This paper explores a quantum penny flip game on a Heisenberg spin chain, demonstrating how players can leverage system complexity and auxiliary spins to improve their outcomes.

Contribution

It introduces a quantum penny flip game on a Heisenberg spin chain and shows how auxiliary spins can be used to influence game dynamics and increase payoffs.

Findings

Players aware of the system's structure can achieve higher payoffs.

Introducing auxiliary spins alters the game dynamics.

Quantum control parameters enable strategic manipulation.

Abstract

We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.