Quantum Illumination Radar 2D: Signal-Space Discrimination

Radar Parameters

Signal brightness N_S 0.010

Background noise N_B 20

Target reflectivity κ 0.05

Trial speed 4 / s

Live Detection Statistics

0.0 dB

quantum advantage (error exponent)

Quantum P(err)

—

Classical P(err)

—

Trials run

Target present

50%

How it works

This is the 2D signal-space counterpart to the 3D quantum-illumination flight simulator: instead of watching a photon fly through a 3D scene, you look directly at the measurement distributions the receiver has to discriminate between — the actual mathematical object detection theory is built on.

Each trial draws one Gaussian-distributed measurement value from either the "target absent" distribution (mean 0) or the "target present" distribution (mean shifted by κ·N_S), for both receivers at once, using the same noise variance ratio as the 3D model:

Classical noise variance:  N_B + 1
Quantum noise variance:   (N_B + 1) / 4

Classical: P_err ≈ ½·exp( −M·κ·N_S /(N_B+1) )
Quantum:   P_err ≈ ½·exp( −4·M·κ·N_S/(N_B+1) )

The top two panels plot the theoretical Gaussian curves for both hypotheses on each receiver, with the decision threshold as a dashed line, and a live strip-plot of every actual trial's measurement value, split into a "target present" row and a "target absent" row, colored green when the receiver's decision matched the truth and red when it didn't. The bottom panel sweeps the error-probability formulas above across target reflectivity κ on a log scale, so the constant 4x gap in the exponent — the entire quantum advantage — is visible as the vertical distance between the two curves at your current κ, not just as a single number.

N_S — mean signal photon number per pulse (higher = brighter probe, both schemes improve).
N_B — thermal background photons per mode (the noisy jamming/clutter the target sits in).
κ — target reflectivity (how much of the signal bounces back).
Run trials — fires paired classical/quantum trials continuously and adds each one's measurement value to its receiver's strip-plot row.

Quantum receiver curve Classical receiver curve Correct decision Detection error