Manuscript Hawk01-A@1 · Hawk01-A.tex · section · 11979653

Three access classes

Observer access, collection, and robust certification › Three access classes · lines 1833–1884

Hawk01-A@1#eq:observercomposition, Hawk01-A@1#eq:geometricfraction, Hawk01-A@1#eq:detectedcounts

For a supplied outgoing channel $N_{u}^{out}$ , the observer sees

N_{u}^{obs} = C_{u} \circ N_{u}^{out},

where $C_{u}$ includes collection, propagation, storage, backgrounds, and any pre-query measurement.

We distinguish:

ideal asymptotic coherent access: all declared outgoing modes and early resource are available;
finite-aperture coherent access: a declared collection channel retains the captured quantum state;
ordinary detection access: a declared complete instrument leaves only classical detector records before the query.

The third is not identified with the second.

For isotropic emission, a small far-field aperture has the geometric estimate

f_{geom} ≃ \frac{A _{det}}{4 π d ^{2}} .

This estimate requires the corresponding angular and wavelength regime. Otherwise mode-overlap and diffraction must be calculated. The expected source-derived detected count is

N_{det} = \int_{u_{0}}^{u_{1}} d u \int_{0}^{\infty} d ω λ \sum η_{λ} (ω, u) \frac{d ^{2} N _{λ}}{d u d ω} .

Background counts are a separate apparatus contribution.

Equation (eq:detectedcounts) is a mean-count forecast, not a coherent decoding channel. A scalar efficiency cannot replace the multimode channel (eq:observercomposition).

Displayed formulas in this passage

Hawk01-A@1#eq:observercomposition · line 1837
$N_{u}^{obs} = C_{u} \circ N_{u}^{out},$
Hawk01-A@1#eq:geometricfraction · line 1860
$f_{geom} ≃ \frac{A _{det}}{4 π d ^{2}} .$
Hawk01-A@1#eq:detectedcounts · line 1868
$N_{det} = \int_{u_{0}}^{u_{1}} d u \int_{0}^{\infty} d ω λ \sum η_{λ} (ω, u) \frac{d ^{2} N _{λ}}{d u d ω} .$

Three access classes

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