论文标题
发散功能和复杂结构的几何形状
Geometry from divergence functions and complex structures
论文作者
论文摘要
在量子力学的几何结构中，我们在产品$ m \ times m $上引入了几乎复杂的结构$ j $，该$ m \ times m $的任何可行的统计歧管$ m $。然后，我们使用$ j $从发散函数中提取$ m \ times m $上的预选形式和类似公制的张量。这些张量可能会返回到$ M $，并且在相对于kullback-leibler相对熵的n维相关，并且在忠实密度操作员相对于VonNeumann-Umann-Umegaki相对的（适当的展开空间）的情况下，我们计算它们。
Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a metric-like tensor on $M\times M$ from a divergence function. These tensors may be pulled back to $M$, and we compute them in the case of an N-dimensional symplex with respect to the Kullback-Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann-Umegaki relative entropy.
