CASE 08 · EVENT STATISTICS

Stop calling every bound “classical” without naming its assumptions.

Quantum optics is a superb exclusion machine. But the exclusion is only as broad as the field and detector model used to derive the inequality.

Antibunching: a real hard wall for standard classical photodetection

For a classical random optical intensity with the usual semiclassical photodetection rule, Cauchy–Schwarz gives the familiar benchmark g²(0) ≥ 1. Observing g²(0)<1 therefore excludes that standard positive-intensity model. This is not a verbal trick. It is a serious statistical constraint.

Standard benchmark: g²(0) ≥ 1
Antibunching target: g²(0) < 1
Perfect single-emitter idealization: g²(0) → 0

The reconstruction route, if one exists, must therefore alter something physical: detector response, source dynamics, the mapping from field intensity to event point process, or the underlying field statistics. Merely saying “continuous wave” does nothing.

HOM: the 50% slogan needs an assumption label

For independent weak coherent pulses under the usual random-phase/intensity-correlation conditions, the HOM visibility is bounded by 50%. Experiments with independent single-photon sources can exceed that benchmark. That is a genuine exclusion of that model class.

But the number 50% is not a universal theorem about every classical field construction. Sadana and collaborators demonstrated a near-100% HOM-like coincidence dip with phase-controlled classical microwave fields. Their own conclusion is not “quantum optics is classical”; the complementarity test still distinguishes the two cases. The lesson for this project is sharper:

A benchmark becomes ontological only after every assumption that creates it is made explicit.

Independent/random-phase weak coherent inputsFamiliar HOM visibility ceiling ≈50%.

Phase-correlated classical pulsesHOM-like dip visibility can approach 100%; the dip alone is no longer sufficient.

Single-photon sourcesCan exceed the weak-coherent benchmark while satisfying source-conditioned event statistics.

Reconstruction burdenReproduce source preparation + detector point process + complementarity tests, not only the dip.

What the detector model owes

A candidate continuous-field ontology must generate waiting times, anticoincidences, dead-time dependence, saturation, detector-efficiency dependence, g²(τ), source conditioning and HOM visibility from explicit material dynamics. If event rules are simply inserted after the field calculation, Q3 remains unearned.

Interactive exclusion lab

The live lab now lets you switch between the standard g² benchmark, a detector-recovery point-process model, independent weak-coherent HOM, and phase-correlated classical HOM-like interference. The point is not to “fake quantum.” It is to see exactly which assumption moves each boundary.

Primary controls

Paul (1982): photon antibunching review
Ou & Mandel (1989): visibility above 50% in two-photon interference
Sadana et al. (2019): near-100% HOM-like dip with classical fields
Chen et al. (2016): 50% limit for independent weak coherent states

The strongest classical-reconstruction argument is not that the bounds are fake. It is that every bound must be attached to its actual model class.