Game-theoretic discovery of quantum error-correcting codes through Nash equilibria

Christoph Roch, Thomy Phan, Sebastian Feld +4 more

Neal Solmeyer, Ricky Dixon, Radhakrishnan Balu

Hoor Banu, K. Raghavendra Rao

Philip V. Fellman, Jonathan Vos Post

Piotr Frąckiewicz, Anna Gorczyca–Goraj, Krzysztof Grzegorz Grzanka +2 more

The concept of Nash equilibria in pure strategies for quantum extensions of the general form of the Prisoner's Dilemma game is investigated. The process of quantization involves incorporating two additional unitary strategies, which effectively expand the classical game. We consider five classes of such quantum games, which remain invariant under isomorphic transformations of the classical game. The resulting Nash equilibria are found to be more closely aligned with Pareto-optimal solutions than those of the conventional Nash equilibrium outcome of the classical game. Our results demonstrate the complexity and diversity of strategic behavior in the quantum setting, providing new insights into the dynamics of classical decision-making dilemmas. In particular, we provide a detailed characterization of strategy profiles and their corresponding Nash equilibria, thereby extending the understanding of quantum strategies' impact on traditional game-theoretical problems.

Adam Lowe

Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilized as a mechanism to witness and determine quantum correlation. By combining quantum theory with Bayesian game theory, a constant-sum game is designed in which the players are competing against each other and crucially gain at the other player’s expense. Subsequently, it is found that mixed strategy Nash equilibria are only necessary when considering quantum correlation for the designed game. This reveals that a Bayesian game-theoretic framework yields a sufficient condition for detecting quantum effects.