量子纠缠和量子操作对CHSH量子博弈优越性的影响

Influence of quantum entanglement and quantum operation on superiority of CHSH quantum game

已有的大多数有关量子博弈的研究只关注粒子处在最大纠缠态和特定的量子操作时模型的优越性.在实际应用中,所用粒子可能偏离最大纠缠态,量子操作也可能存在一定的偏差。基于此,研究了这两方面对CHSH量子博弈模型优越性的影响。结果表明,当粒子处在特定纠缠态时,量子获胜概率P并不总是大于经典获胜概率P_c,采用不同的量子旋转门操作可以达到的最大量子获胜概率P_(max)随着量子态纠缠度的增大而增大。在P_(max)对应的量子门旋转角附近,某些旋转角范围对应的P变化较小。这些研究对量子博弈的应用提供了理论指导。

Recently, quantum game has attracted more and more attention. Most of the studies focused on the advantages of quantum game in the case of the maximally entangled states and the certain quantum operations. In practice, the particles may not in the maximally entangled state and there are some quantum operation deviations. For this, the two factors are considered in CHSH game. It is found that when particles are in general entangled quantum states, the probability of winning for quantum strategy P is not always greater than that for classical strategy Pc, therefore suitable quantum operations should be chosen to satisfy P 〉 Pc. The maximum of the probability of winning for quantum strategy Pmax increases with the degree of entanglement of quantum states. For some angle regions that near the angle corresponding to Pmax, P change slightly. All these results provide theoretical guidance for quantum games.