The additivity of the minimal output entropy and that of the $χ$-capacity are known to be equivalent for finite-dimensional irreducibly covariant channels. In this paper we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to Bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper \cite{ghg} to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimode generalization of the "threshold condition", obtained for single mode in \cite{schaefer}) and the proof of the fact that under this condition the classical "Gaussian capacity" resulting from optimization over Gaussian inputs is equal to the full classical capacity. We also investigate implications of the gauge-covariance condition for the single- and multimode Bosonic Gaussian channels.
No advantage from classical assistance for energy-constrained bosonic dephasing channels
Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo（量子计算研究所与物理和天文学系，滑铁卢大学）；Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo（量子计算研究所与应用数学系，滑铁卢大学）
Classical capacities under physical constraints: More capacity with less entanglement
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-昌德拉研究所，霍米·巴巴国立学院成员）；QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong（香港大学计算机科学系量子信息计算倡议）
Efficiently computable bounds on the energy-constrained quantum reading capacity
RIKEN Pioneering Research Institute（理化学研究所先驱研究机构）；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RMIT University（皇家墨尔本理工大学）；Cornell University（康奈尔大学）
