We propose a generalization of the quantum relative entropy by considering the geodesic on a manifold formed by all the invertible density matrices $ \mathcal{P} $. This geodesic is defined from a deformed exponential function $ \varphi $ which allows to work with a wider class of families of probability distributions. Such choice allows important flexibility in the statistical model. We show and discuss some properties of this proposed generalized quantum relative entropy.

中文翻译：

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广义量子相对熵

通过考虑由所有可逆密度矩阵$ \ mathcal {P} $形成的流形上的测地线，我们提出了量子相对熵的一般化。该测地线是从变形指数函数$ \ varphi $定义的，该指数函数允许使用更广泛的几类概率分布。这种选择为统计模型提供了重要的灵活性。我们展示并讨论了该提议的广义量子相对熵的一些性质。