Canonical Divergence for Flat αConnections: Classical and Quantum
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.
 Publication:

Entropy
 Pub Date:
 August 2019
 DOI:
 10.3390/e21090831
 arXiv:
 arXiv:1907.11122
 Bibcode:
 2019Entrp..21..831F
 Keywords:

 Mathematical Physics
 EPrint:
 18 pages