Quantum Illumination Parameter-Space & Detection Statistics (2D)

Receiver Mode

Scenario Parameters

Target reflectivity η 5.0%

Background thermal photons N_B 3.0

Signal brightness N_S 0.10

Integration window M 200 pulses

Detection Statistics

Error exponent κ (active mode)

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Quantum advantage

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P(error) after M pulses

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Pulses emitted

How this 2D view differs from the 3D scene

The 3D version animates individual photon "particles" flying between a source and a target and tallies hits into two progress bars — a literal, camera-view dramatization. This 2D version drops the flattened scene entirely and instead renders the actual mathematical objects of the quantum-illumination hypothesis test directly:

Top-left — gain heatmap. A 2D field over (N_S, N_B) space, colored by the quantum error-exponent gain and its dB advantage, computed on a log–log grid independent of any animation. The crosshair marks your current sliders.
Top-right — Chernoff decay curves. P_e(M) plotted on a log axis for both receivers across the full integration-window range, with a marker at your chosen M — showing directly why the quantum exponent's steeper slope wins for large M.
Bottom — live receiver traces. Two independently-run Monte Carlo pulse accumulators (their own RNG loop, not read from the 3D scene) scroll in real time, resetting every M pulses exactly like a real integrate-and-dump receiver.

All three panels share the same closed-form model as the literature's qualitative scaling (Lloyd 2008; Tan et al. 2008):

P_e(M) ≈ (1/4) · exp(-M·κ)
κ_classical = η·N_S / (2·N_B + 1)
gain(N_S,N_B) = 1 + 3 · [1/(1+N_S)] · [N_B/(1+N_B)]
κ_quantum = gain · κ_classical
advantage (dB) = 10·log10(gain)

The gain formula depends only on N_S and N_B (never η), which is exactly why the heatmap is static while η only shifts the decay curves — a relationship the 3D particle scene never makes visible.

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