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arXiv · 1907.11122

Canonical divergence for flat $\alpha$-connections: Classical and Quantum

Domenico Felice·Nihat Ay
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Abstract

A recent canonical divergence, which is introduced on a smooth manifold $\mathrm{M}$ endowed with a general dualistic structure $(\mathrm{g},\nabla,\nabla^*)$, is considered for flat $\alpha$-connections. In the classical setting, we compute such a canonical divergence on the manifold of positive measures and prove that it coincides with the classical $\alpha$-divergence. In the quantum framework, the recent canonical divergence is evaluated for the quantum $\alpha$-connections on the manifold of all positive definite Hermitian operators. Also in this case we obtain that the recent canonical divergence is the quantum $\alpha$-divergence.

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Domenico Felice, Nihat Ay. 2019-07-25. Canonical divergence for flat $\alpha$-connections: Classical and Quantum. https://doi.org/10.3390/e21090831

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