论文标题
量子信息启发
Quantum Information Elicitation
论文作者
论文摘要
在经典的评分规则设置中，主体激励代理人真实地报告他们对未来结果的概率信念。本文解决了这种私人信念而不是经典概率分布而不是量子混合状态的情况。在最终的量子评分规则设置中，主体选择得分函数和测量函数，而代理则响应其报告的密度矩阵。提出了量子评分规则的几种特征，这些特征揭示了基于凸分析的熟悉结构。光谱得分，其中测量函数是通过报告的密度矩阵的光谱分解给出的，具有特别优雅的结构，并连接到量子信息理论。转向财产启发，这种信念的特征向量是可取的，而特征值和熵具有最大的启发复杂性。本文以讨论其他量子信息引发设置和与文献的联系的讨论结束。
In the classic scoring rule setting, a principal incentivizes an agent to truthfully report their probabilistic belief about some future outcome. This paper addresses the situation when this private belief, rather than a classical probability distribution, is instead a quantum mixed state. In the resulting quantum scoring rule setting, the principal chooses both a scoring function and a measurement function, and the agent responds with their reported density matrix. Several characterizations of quantum scoring rules are presented, which reveal a familiar structure based on convex analysis. Spectral scores, where the measurement function is given by the spectral decomposition of the reported density matrix, have particularly elegant structure and connect to quantum information theory. Turning to property elicitation, eigenvectors of the belief are elicitable, whereas eigenvalues and entropy have maximal elicitation complexity. The paper concludes with a discussion of other quantum information elicitation settings and connections to the literature.
