2019/07/31 by Domenico Felice, Nihat Ay
Mathematics · Physics and Astronomy · #Classical capacity #Divergence (linguistics) #Hermitian matrix #Manifold (fluid mechanics) #Mathematical Inequalities and Applications #Mathematics #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum channel #Quantum information #Quantum mechanics #Statistical Mechanics and Entropy #math-ph #math.MP
paper · pdf · doi:10.3390/e21090831
18 pages
openalex created_date 2019/07/30 · arxiv created 2019/08/23 · openalex publication_date 2019/08/25 · arxiv updated 2019/10/02 · openalex updated_date 2026/08/05
A recent canonical divergence, which is introduced on a smooth manifold M endowed with a general dualistic structure ( g , ∇ , ∇ * ) , is considered for flat α -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 α -divergence. In the quantum framework, the recent canonical divergence is evaluated for the quantum α -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 α -divergence.