发表机构
Shanghai Jiao Tong University; Cornell University（上海交通大学; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于相对熵最小变化原理，建立量子统计推断中最优测量的闭式表征，恢复了两类已知测量并发现软最小热测量新家族，还证明该原理的可加性并研究了费米-狄拉克热测量的量子假设检验性能。
AI 中文摘要
最小变化原理在经典概率论中为贝叶斯逆转信道提供了信息论表征，近期被提议作为将贝叶斯规则扩展至量子信息论的框架。本文利用量子相对熵，针对量子统计推断场景研究最小变化原理。具体而言，我们考虑基于经典到量子制备信道的正向过程，以及基于量子到经典测量信道的逆向过程。我们建立了该原理下最优测量的闭式表征，且该最优测量可通过包含单个无约束厄米变量的对偶形式求解。该视角使我们能在同一框架内恢复若干著名测量，包括良好测量（pretty good measurements）和费米-狄拉克热测量，并借此发现一类新的家族，我们称之为软最小热测量（softmin thermal measurements）。我们进一步证明，软最小热测量是熵正则化半定优化问题的最优解，表明它们在测量中的作用类似于统计力学中热态的作用。最后，我们证明了相对熵最小变化原理的可加性性质，并研究了费米-狄拉克热测量在量子假设检验中的性能。
英文摘要
The minimum change principle provides an information-theoretic characterization of the Bayes reversal channel in classical probability theory and has recently been proposed as a framework for extending Bayes' rule to quantum information theory. Using quantum relative entropy, we investigate a minimum change principle for the setting of quantum statistical inference. Specifically, we consider a forward process based on a classical-to-quantum preparation channel and a reverse process based on a quantum-to-classical measurement channel. We establish a closed-form characterization of measurements that are optimal for this principle, and this optimal measurement can be found via a dual formulation involving a single unconstrained Hermitian variable. This perspective allows us to recover some notable measurements within the same framework, including pretty good measurements and Fermi-Dirac thermal measurements, and we use it to discover a novel family that we call softmin thermal measurements. We further show that softmin thermal measurements arise as optimal solutions to entropy-regularized semidefinite optimization problems, demonstrating that they play a role for measurements analogous to that of thermal states in statistical mechanics. Finally, we prove an additivity property for the relative-entropy minimum change principle and investigate the performance of Fermi-Dirac thermal measurements for quantum hypothesis testing.
Comments38 pages
