What was already known
Guha, Erkmen and Shapiro conjectured this photon-number inequality. Earlier work established special input cases and a different, weaker quantum entropy-power inequality.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Proves the conjectured entropy photon-number inequality in its finite-energy multimode setting.
Limitations
Inputs must be independent but may be internally entangled across modes. The paper’s thermal-channel and broadcast-capacity consequences are outside the selected Lean statement.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves the full two-input finite-energy beam-splitter inequality for any finite number of modes.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For two independent finite-mean-energy bosonic inputs with any finite positive number of modes, beam-splitter output satisfies N(ρC)≥ηN(ρA)+(1−η)N(ρB) for 0≤η≤1, where N(ρ)=g⁻¹(S(ρ)/n) is entropy photon number per mode.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision