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arXiv:2406.08412 · Physical Review Letters

Experimental Quantum Advantage in the Odd-Cycle Game

P. Drmota, D. Main, E. M. Ainley, A. Agrawal, G. Araneda, D. P. Nadlinger, B. C. Nichol, R. Srinivas, Adán Cabello, D. M. Lucas

Published Feb 21, 2025• 4 citations
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Abstract

We report the first experimental demonstration of the odd-cycle game. We entangle two atoms separated by ∼2 m, and the players use them to win the odd-cycle game with a probability ∼26σ above that allowed by the best classical strategy. The experiment implements the optimal quantum strategy, is free of loopholes, and achieves 97.8(3)% of the theoretical limit to the quantum winning probability. We perform the associated Bell test and measure a nonlocal content of 0.54(2)-the largest value for physically separate devices, free of the detection loophole, ever observed.

DOI
10.1103/physrevlett.134.070201

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We report the first experimental demonstration of the odd-cycle game. We entangle two atoms separated by ∼2 m, and the players use them to win the odd-cycle game with a probability ∼26σ above that allowed by the best classical strategy. The experiment implements the optimal quantum strategy, is free of loopholes, and achieves 97.8(3)% of the theoretical limit to the quantum winning probability. We perform the associated Bell test and measure a nonlocal content of 0.54(2)-the largest value for physically separate devices, free of the detection loophole, ever observed.
Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our game has a fair quantum equilibrium with higher payoffs for both players than in any fair classical equilibrium. Finally, we play the game using a commercial entangled photon source and demonstrate experimentally the quantum advantage.
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Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
We propose and experimentally demonstrate a zero-sum game that is in a fair Nash equilibrium for classical players, but has the property that a quantum player can always win using an appropriate strategy. The gain of the quantum player is measured experimentally for different quantum strategies and input states. It is found that the quantum gain is maximized by a maximally entangled state, but does not decrease to zero when entanglement disappears. Instead, it links with another kind of quantum correlation described by discord for the qubit case and the connection is demonstrated both theoretically and experimentally.
We propose and experimentally demonstrate a zero-sum game that is in a fair Nash equilibrium for classical players, but has the property that a quantum player can always win using an appropriate strategy. The gain of the quantum player is measured experimentally for different quantum strategies and input states. It is found that the quantum gain is maximized by a maximally entangled state, but does not decrease to zero when entanglement disappears. Instead, it links with another kind of quantum correlation described by discord for the qubit case and the connection is demonstrated both theoretically and experimentally.
Prior to this work, the largest known gap between the entangled value and the classical value for a one-round two-player nonlocal game with a perfect entangled strategy using two Bell states of entanglement was 19\frac{1}{9}91​, achieved by the Mermin-Peres magic square game. A larger gap of 215\frac{2}{15}152​ has been claimed for the related doily game of Kelleher, Roomy, and Holweck (Quant. Inf. Proc., 2024). However, this value assumes that the classical players use identical local strategies, and we show that dropping this assumption reduces the gap back to 19\frac{1}{9}91​. We then demonstrate that 19\frac{1}{9}91​ is not optimal by explicitly constructing a new nonlocal game with gap 435\frac{4}{35}354​.