Abstract

We study positive operator-valued measures by algebraic and geometric methods. We prove that positive operator-valued measures are parametrized by a Poisson manifold. Also, we show how to obtain symplectic leaves of this Poisson manifold in terms of parameters of the measures. In addition, we study the interaction of two projection-valued measures by the methods of algebraic geometry.

中文翻译：

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量子测量的一些代数和几何方面

摘要

我们通过代数和几何方法研究正算子值度量。我们证明了正运算符值度量由泊松流形参数化。此外，我们展示了如何根据测度参数获得这个泊松流形的辛叶。此外，我们通过代数几何的方法研究了两个投影值度量的相互作用。