Quantum repeated games

重复CHSH游戏经典值的最优界

Optimal bounds on the classical value of the repeated CHSH game

该研究确定了重复CHSH游戏经典值的最优界，结合已有下界得到其渐近精确值，并证明存在经典-量子值差距的异或游戏，其重复游戏渐近值也存在对应差距。

作为随机博弈的重复量子博弈：未来阴影与纠缠的影响

Repeated quantum game as a stochastic game: Effects of the shadow of the future and entanglement

本文研究无限次重复量子博弈，证明其可映射为随机博弈，并发现纯反应性策略的支撑集不可数无限，策略优劣取决于折扣因子与纠缠程度，且量子设定下以牙还牙可在高折扣因子时击败始终背叛策略。

Quantum Repeated Interactions and the Chaos Game

Inspired by the algorithm of Barnsley's chaos game, we construct an open quantum system model based on the repeated interaction process. We shown that the quantum dynamics of the appropriate fermionic/bosonic system (in interaction with an environment) provides a physical model of the chaos game. When considering fermionic operators, we follow the system's evolution by focusing on its reduced density matrix. The system is shown to be in a Gaussian state (at all time $t$) and the average number of particles is shown to obey the chaos game equation. Considering bosonic operators, with a system i…

Quantum repeated games revisited

We present a scheme for playing quantum repeated 2x2 games based on the Marinatto and Weber's approach to quantum games. As a potential application, we study twice repeated Prisoner's Dilemma game. We show that results not available in classical game can be obtained when the game is played in the quantum way. Before we present our idea, we comment on the previous scheme of playing quantum repeated games.

The Parallel-Repeated Magic Square Game is Rigid

We show that the $n$-round parallel repetition of the Magic Square game of Mermin and Peres is rigid, in the sense that for any entangled strategy succeeding with probability $1 -\varepsilon$, the players' shared state is $O(\mathrm{poly}(n\varepsilon))$-close to $2n$ EPR pairs under a local isometry. Furthermore, we show that, under local isometry, the players' measurements in said entangled strategy must be $O(\mathrm{poly}(n\varepsilon))$ close to the "ideal" strategy when acting on the shared state.

无限重复量子博弈与策略效率

Infinitely Repeated Quantum Games and Strategic Efficiency

本文建立一般重复量子博弈概念并证明量子民间定理，揭示强纠缠下量子囚徒困境中经典 Pareto 最优与相互合作未必构成均衡，并给出具体均衡策略。