The unassisted classical capacity of the generalized amplitude-damping channel

Claims that for every $\gamma,\nu\in[0,1]$ the unassisted classical capacity of $\mathcal A_{\gamma,\nu}$ equals its one-shot Holevo capacity, given by $\max_{p\in[0,1]}[h((1-\gamma)p+\gamma\nu)-g(\gamma\nu(1-\nu)+\gamma(1-\gamma)(p-\nu)^2)]$ in bits, with $g$ the entropy of a qubit state of given determinant, attained by two equiprobable pure signals of opposite phase and their independent products. It also claims additivity of one-shot Holevo capacity, minimum output entropy and regularized classical capacity under tensoring with any finite-dimensional channel. It does NOT give the quantum or private capacity of the channel, entanglement-assisted settings, or a closed form for the maximizing $p$.

Claims that for every $\gamma,\nu\in[0,1]$ the unassisted classical capacity of $\mathcal A_{\gamma,\nu}$ equals its one-shot Holevo capacity, given by $\max_{p\in[0,1]}[h((1-\gamma)p+\gamma\nu)-g(\gamma\nu(1-\nu)+\gamma(1-\gamma)(p-\nu)^2)]$ in bits, with $g$ the entropy of a qubit state of given determinant, attained by two equiprobable pure signals of opposite phase and their independent products. It also claims additivity of one-shot Holevo capacity, minimum output entropy and regularized classical capacity under tensoring with any finite-dimensional channel. It does NOT give the quantum or private capacity of the channel, entanglement-assisted settings, or a closed form for the maximizing $p$.