Qubit flip game on a Heisenberg spin chain

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.Comment: 13 pages, 3 figures, 3 table

Decoherence effects in the quantum qubit flip game using Markovian approximation

“…The corruption of quantum states in schemes implementing quantum games was studied by various authors, e.g., in [4], the authors study the general treatment of decoherence in two-player, two-strategy quantum games; in [5], the authors perform an analysis of the two-player prisoners' dilemma game; in [6], the multiplayer quantum minority game with decoherence is studied; in [7,8], the authors analyze the influence of the local noisy channels on quantum Magic Squares games, while the quantum Monty Hall problem under decoherence is studied first in [9] and subsequently in [10]. In [11], the authors study the influence of the interaction of qubits forming a spin chain on the qubit flip game. An analysis of trembling hand-perfect equilibria in quantum games was done in [12].…”

“…The problem with the above procedure is that it separates unitary evolution from the decoherent evolution. In Miszczak et al [11], it was proposed to observe the behavior of the quantum version of the penny flip game under more physically realistic assumptions where decoherence due to coupling with the environment and unitary evolution happen simultaneously. In the papers, the authors study an implementation of the qubit flip game on quantum spin chains.…”

“…In this work, our goal is to follow the work done in [11] and to discuss the quantum penny flip game as a physical experiment consisting in preparation, evolution and measurement of the system. For the purpose of this paper, we assume that preparation and measurement, contrary to noisy evolution of the system are perfect.…”

“…It was also shown, that if Alice was allowed to extend her set of strategies to quantum strategies she could always win. In Miszczak et al [11] it was shown that when both players have access to quantum strategies the game becomes fair and it has the Nash equilibrium.…”

“…In our study, we wish to follow the work done in the aforementioned paper [11]. Hence, we consider a quantum version of the penny flip game.…”