Experimental observation of phase-transition-like behavior in an optical simulation of single-qubit game
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Experimental observation of phase-transition-like behavior in an optical simulation of single-qubit game M. H. M. Passos1,2 · G. S. G. P. Tiago1,2 · M. A. de Ponte3 · Alan C. Santos4 · J. A. O. Huguenin1,2 Received: 22 April 2020 / Accepted: 1 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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 singlequbit 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. Keywords Quantum game · Linear optics · Phase-transition-like
1 Introduction For decision-making problems, a powerful approach is game theory. Conflict situations can be mathematically modeled in order to explore possible solutions. Different scenarios was studied giving rise to games as prisoner dilemma [1], Colonel Blotto game [2], evolutionary games [3] and auction [4], to cite a few. In quantum realm, Meyer [5] and, independently, Eisert et al. [6] established in 1999 a new mark in game theory by introducing quantum strategies in the prisoner dilemma. Such approach showed
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J. A. O. Huguenin [email protected]
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advantages for players with access to quantum strategies. Then, several games were revisited in order to explore the quantum counterpart. Monty Hall problem [7], quantum auctions [8], battle of sexes [9] and quantum duel [10,11] are some examples of well-known quantum games. Experimental realization of quantum games strategies has been performed with different systems. The prisoner dilemma was implemented first in a nuclear magnetic resonance (NMR) experiment [12]. The Aharonov–Vaidman quantum game was implemented with a Young-type photonic qutrit [13]. Single-photon system was proposed to implement two players quantum games [14] as well as a proposal to implement the simultaneous quantum duel with twin photons produced by spontaneous parametric down-conversion [15]. Quantum games were also emulated with modes
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