Experimental observation of phase-transition-like behavior in an optical simulation of single-qubit game

Phase-transition-like behavior in quantum games has been studied in recent years as a strategy to deal with abrupt changes in the expected payoff of quantum players. More precisely, such behavior is investigated in the context of two-qubit quantum games, where entanglement is used as a resource for quantum players or quantum game referees. In this work, we present the first experimental realization of a single-qubit game where phase-transition-like behavior raises as an immediate consequence of quantum coherence, since no entanglement is present in our game. The game was realized by encoding the qubit in the polarization degree of freedom of an intense laser beam. We investigate the optimal gain of the quantum player as well as a discussion and obtaining of critical points that was experimentally observed, where we had an excellent agreement between theoretical predictions and the experimental results. Due to the power of the quantum-classical analogy between quantum states and optical modes, our platform is adequate to simulate the quantum game and our experiment can be efficiently reproduced in a single-photon experiment.