In the present paper we study the entropy gain $H(Φ[ρ])-H(ρ)$ for infinite-dimensional channels $Φ$. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty of channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.
Generalized Entropy Approach for Conserved Systems with Finite vs Infinite Entities: Insights into Non-Gaussian and Non-Chi-Square Distributions using Havrda-Charvát-Tsallis Entropy vs Gaussian Distributions via Boltzmann-Shannon Entropy
Entropy Production for Stationary Diffusions on Hilbert Spaces
Institute for Functional Intelligent Materials, National University of Singapore（新加坡国立大学功能智能材料研究所）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
Gaussian concentration, integral probability metrics, and coupling functionals for infinite lattice systems
Centre de Physique Théorique, CNRS, Ecole polytechnique, Institut Polytechnique de Paris（理论物理中心，法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）；Institute of Applied Mathematics, TU Delft（应用数学研究所，代尔夫特理工大学）
