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A generalized quantum relative entropy

  • * Corresponding author: Luiza H. F. Andrade

    * Corresponding author: Luiza H. F. Andrade 
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  • 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.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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