The unassisted classical capacity of the generalized amplitude-damping channel

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This event attributed to Unreleased internal OpenAI model

Leditzky, Kaur, Datta and Wilde (2018), where the amplitude-damping capacity is listed as open evidence for this event

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 $p$. parent of this event

Lean formalization: Holevo additivity and capacity of generalized amplitude damping evidence for this event

Lean comparator statement: AmplitudeDamping evidence for this event

The unassisted classical capacity of the generalized amplitude-damping channel parent of this event

The unassisted classical capacity of the generalized amplitude-damping channel evidence for this event

VibeMathed record: The unassisted classical capacity of the generalized amplitude-damping channel evidence for this event