quantum optics decoded — beam-splitter unitary, Hong–Ou–Mandel bunching, g²(0) antibunching
Theorem.quantum optics decoded — beam-splitter unitary, Hong–Ou–Mandel bunching, g²(0) antibunching.
Proof.the genuine quantum optics of light (user, 2026-07-25: "quantum optics"). A 50/50 beam splitter is the real orthogonal unitary U = [[1,1],[1,−1]]/√2 with UᵀU = I, a genuine quantum gate on the two modes. Hong–Ou–Mandel: two indistinguishable photons entering it always exit the SAME port because the coincidence (c†d†) amplitude r²−t² = 0 vanishes — a two-photon interference (the HOM dip) with no classical analogue. The second-order coherence g²(0) separates quantum from classical light: 1 for coherent (Poissonian), 2 for thermal (super-Poissonian, bunched), and 1−1/n = 0 for a single-photon Fock state (antibunched); g²(0)<1 has NO classical (positive-P) model — every classical field has g²(0) ≥ 1 — so antibunching is the definitive signature of quantised light. SCOPE: this computes the standard quantum-optics results as a MODEL over the sealed algebra — genuine quantum-optics mathematics but a classical simulator, not a photon-counting experiment and not a real single-photon source. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#quantumOpticsDecoded
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"quantum optics decoded — beam-splitter unitary, Hong–Ou–Mandel bunching, g²(0) antibunching" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation quantumOpticsDecoded.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (quantumOpticsDecoded @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes quantumOpticsDecoded (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.