论文标题
量子统计推断的几何方法
Geometric approach to quantum statistical inference
论文作者
论文摘要
我们研究了假设检验的量子统计推断任务及其规范变化，以审查其功绩相应数字之间的关系 - 统计距离的衡量标准 - 并证明与经典环境相比，这在量子制度中产生了至关重要的差异。在我们的分析中，我们主要关注数据推断问题的几何方法，在该方法中，可以将上述措施整洁地解释为特定形式的差异形式，这些差异形式可以量化概率分布空间中的距离，或者在处理量子系统时，密度矩阵的差异。此外，在Riemannian几何形状的标准语言的帮助下，我们确定了这些差异必须诱导的指标，并且这些指标必须自然继承。最后，我们讨论了这种几何方法对量子参数估计问题，“速度极限”和热力学问题的示例应用。
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial differences which arise in the quantum regime in contrast to the classical setting. In our analysis, we primarily focus on the geometric approach to data inference problems, within which the aforementioned measures can be neatly interpreted as particular forms of divergences that quantify distances in the space of probability distributions or, when dealing with quantum systems, of density matrices. Moreover, with help of the standard language of Riemannian geometry we identify both the metrics such divergences must induce and the relations such metrics must then naturally inherit. Finally, we discuss exemplary applications of such a geometric approach to problems of quantum parameter estimation, "speed limits" and thermodynamics.
