The maximally entangled (ME) Eisert–Wilkens–Lewenstein (EWL) quantization scheme efficiently solves the classical prisoner’s dilemma (PD). Despite the intensive research on the EWL scheme, little is known about the role of the arbiter in controlling the scheme properties. We redefine the EWL scheme by introducing an arbitrary phase shift into the ME initial state. Four basic initial states were analyzed in this study. It is found that the arbiter completely controls the characteristics of the arbitrary ME quantum PD. The arbiter can adjust the ME initial state to obtain an efficient symmetric Nash equilibrium. In contrast, the arbiter can nullify the quantization advantages. Moreover, it can preserve/violate the symmetry of the game or even turn it into a potential game.

中文翻译：

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任意最大纠缠量子囚徒困境

最大纠缠 (ME) Eisert–Wilkens–Lewenstein (EWL) 量化方案有效解决了经典的囚徒困境 (PD)。尽管对 EWL 方案进行了深入研究，但对于仲裁器在控制方案属性中的作用知之甚少。我们通过在 ME 初始状态中引入任意相移来重新定义 EWL 方案。本研究分析了四种基本初始状态。发现仲裁器完全控制任意ME量子PD的特性。仲裁者可以调整ME初始状态以获得有效的对称纳什均衡。相反，仲裁器可以抵消量化优势。而且，它可以保留/破坏游戏的对称性，甚至将其变成一个潜在的游戏。