OpenAI reports the entropy photon-number inequality

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.

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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.

Why it matters

If correct, proves the conjectured entropy photon-number inequality in its finite-energy multimode setting.

What counts as progress

Does entropy photon number satisfy the beam-splitter mixing inequality?

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