OpenAI · 276-01 · 2026-09-24 · Mathematical physics
Classical capacity and entropy inequalities for generalized amplitude damping
preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026
Family 276. The classical capacity of generalized amplitude damping.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Determines the unassisted classical capacity of every qubit generalized amplitude-damping channel, including all damping and thermal parameters. An explicit one-variable optimization gives the capacity, attained by independent two-state signal ensembles with collective decoding. Holevo capacity, minimum output entropy and regularized classical capacity are additive when tensoring with any finite-dimensional quantum channel.
We determine the unassisted classical capacity of every qubit generalized amplitude-damping channel, for all damping strengths and thermal occupations. It equals the one-shot Holevo capacity and is given by a one-variable maximum. A binary pure-state ensemble attains the one-use optimum, and its independent products attain the optimum at every block length. We also prove that one-shot Holevo capacity, minimum output entropy, and regularized unassisted classical capacity are additive under tensor product with every finite-dimensional completely positive trace-preserving partner channel.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 276: Classical capacity of generalized amplitude damping. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
AmplitudeDamping.lean · AmplitudeDamping.lean
Page curve
A one-use Holevo interval is not a Page curve
Family 276 records the classical capacity of every qubit generalized amplitude-damping channel. Oai276-A records a conditional one-use audit and does not verify 276-01. The finite certificate is not partner additivity, not a quantum capacity, and not a secret-key theorem. AmplitudeDamping.lean is not this certificate. A static Holevo record is not a Page curve. A channel that is not entanglement breaking is not gravity-generated entanglement and not an exclusion of classical gravity. The authors of the external preprint are OpenAI. The companion does not verify those proofs.
Page curveOai276-A one-use Holevo certificateEn07-C thermal inputEm03-F entanglement-breaking specimen