论文标题
格里森框架功能的概括用于量子测量
A Generalization of Gleason's Frame Function for Quantum Measurement
论文作者
论文摘要
目的是将格里森（Gleason）的框架功能的概念扩展到量子测量中的基本定理中必不可少的概念，并将其作用于1紧密，所谓的parseval框架上的更通用的功能。我们将这些功能称为parseval框架的Gleason函数。我们概括的原因是积极的算子有价值的度量（POVM）基本上等同于parseval框架，并且POVM自然而然地在量子测量理论中出现。我们证明，在适当的假设下，parseval框架的格里森功能是二次形式，以及其他类似于格里森的原始定理的结果。此外，我们解决了与格里森功能有关的固有问题，用于不同长度的旁观框架。我们使用该解决方案来削弱Busch定理的有限维度版本中的假设，该假设本身就是Gleason对量子状态的数学表征的类似物。
The goal is to extend Gleason's notion of a frame function, which is essential in his fundamental theorem in quantum measurement, to a more general function acting on 1-tight, so-called, Parseval frames. We refer to these functions as Gleason functions for Parseval frames. The reason for our generalization is that positive operator valued measures (POVMs) are essentially equivalent to Parseval frames, and that POVMs arise naturally in quantum measurement theory. We prove that under the proper assumptions, Gleason functions for Parseval frames are quadratic forms, as well as other results analogous to Gleason's original theorem. Further, we solve an intrinsic problem relating Gleason functions for Parseval frames of different lengths. We use this solution to weaken the hypotheses in the finite dimensional version of Busch's theorem, that itself is an analog of Gleason's mathematical characterization of quantum states.
