纠缠N光子态用于公平和最优的社会决策
Entangled N-photon states for fair and optimal social decision making
摘要：
涉及实体之间资源竞争的情况可以通过竞争性多臂强盗（CMAB）问题来建模，该问题涉及社会问题，例如最大化总结果和实现个体之间最公平的资源再分配。在这些方面，量子态的内在随机性和全局性质为获得该问题的最优解提供了理想的工具。基于先前对双臂两人情形下的CMAB问题的研究，本文提出了寻找偏振纠缠N光子态所需的理论原则，该理论原则可以优化总资源输出，同时确保参与者之间的平等。这些原则被应用到两个，三个，四个和五个球员的情况下，通过使用数值模拟再现现实的配置，并找到最佳的策略，以克服潜在的球员的偏振测量系统之间的不对准。虽然这里没有给出N-玩家情况下的一般公式，但提出了一般推导规则和验证算法。这份报告展示了量子态在有限的概率资源的集体决策中的潜在可用性，这可以作为基于量子的资源分配系统的第一步。
英文摘要：
Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. In these respects, the intrinsic randomness and global properties of quantum states provide ideal tools for obtaining optimal solutions to this problem. Based on the previous study of the CMAB problem in the two-arm, two-player case, this paper presents the theoretical principles necessary to find polarization-entangled N-photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Although a general formula for the N-player case is not presented here, general derivation rules and a verification algorithm are proposed. This report demonstrates the potential usability of quantum states in collective decision making with limited, probabilistic resources, which could serve as a first step toward quantum-based resource allocation systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
