论文标题
w* - 代理上的参数模型和信息几何形状
Parametric models and information geometry on W*-algebras
论文作者
论文摘要
我们在可能的无限二维w* - 代数上介绍了正常正线性函数的平滑参数模型的概念，从而概括了经典和量子信息几何学中使用的参数模型的概念。然后，我们使用在这种情况下自然可用的Jordan产品，以定义有关参数模型的Riemannian度量张量，以符合适当的规律性条件。这种riemannian度量张量会简化为Fisher-Rao度量张量，或fubini-study公制张量，或者在适当选择W*-Algebra选择时，将其用于Burs-Helstrom度量标准张量。
We introduce the notion of smooth parametric model of normal positive linear functionals on possibly infinite-dimensional W*-algebras generalizing the notions of parametric models used in classical and quantum information geometry. We then use the Jordan product naturally available in this context in order to define a Riemannian metric tensor on parametric models satsfying suitable regularity conditions. This Riemannian metric tensor reduces to the Fisher-Rao metric tensor, or to the Fubini-Study metric tensor, or to the Bures-Helstrom metric tensor when suitable choices for the W*-algebra and the models are made.
