{"id":"openai-math/The-entropy-photon-number-inequality","pdf":"https://github.com/openai/math/blob/main/preprints/The-entropy-photon-number-inequality-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-entropy-photon-number-inequality-September-24-2026","tags":["quantum-information","information-theory","bosonic-channels"],"score":0,"title":"The entropy photon-number inequality","domain":"Mathematical physics","family":"273","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove the entropy photon-number inequality for two independent bosonic inputs with finite mean energy, for every finite number of modes. This resolves the entropy photon-number conjecture in this finite-energy setting while allowing arbitrary entanglement among the modes within either input. As a consequence, we determine the exact minimum output entropy at fixed input entropy for every finite tensor power of an identical thermal attenuator, over finite-energy inputs that may be entangled across modes. We also obtain the exact classical capacity region of the degraded two-receiver…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The entropy photon-number inequality"}