利用有限几何结构提高 Mermin 类游戏中的量子优势

量子游戏体现了量子现象（如纠缠和情境性）的非直觉后果。Mermin-Peres 游戏是一个简单例子，展示了两个玩家如何利用共享的量子信息来赢得一个无通信游戏，其中经典玩家无法做到。In this paper we look at the geometric structure behind such classical strategies, and borrow ideas from the geometry of symplectic polar spaces to maximise this quantum advantage. We introduce a new game called the Eloily game with a quantum-classical success gap of $0.2\overline{6}$, larger than that of the Mermin-Peres and doily games. We simulate this game in the IBM Quantum Experience and obtain a success rate of $1$, beating the classical bound of $0.7\overline{3}$ demonstrating the efficiency of the quantum strategy.