Canonical Divergence for Flat α-Connections: Classical and Quantum

A recent canonical divergence, which is introduced on a smooth manifold [Formula: see text] endowed with a general dualistic structure [Formula: see text] , is considered for flat [Formula: see text]-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 [Formula: see text]-divergence. In the quantum framework, the recent canonical divergence is evaluated for the quantum [Formula: see text]-connections on the manifold of all positive definite Hermitian operators. In this case as well, we obtain that the recent canonical divergence is the quantum [Formula: see text]-divergence.