Quantum illumination (Lloyd, 2008; Tan et al., 2008) entangles a signal photon with an idler photon, sends only the signal out to probe a target through a lossy, noisy path, and keeps the idler at the receiver. Even though the round trip's loss and background thermal noise destroy the signal–idler entanglement long before the light returns, a joint measurement of the returned signal against the retained idler still beats any classical (unentangled coherent-state) radar of the same transmitted energy — because the original correlations were stronger than any classical source can produce.
In the low-brightness, high-noise regime (NS ≪ 1, NB ≫ 1) the discrimination error probability for M signal-idler mode pairs against a target of reflectivity κ follows a Chernoff-type exponential bound:
Classical (coherent-state) radar:
P_err ≈ ½ · exp( −M·κ·N_S / (N_B+1) )
Quantum illumination (optimum joint receiver):
P_err ≈ ½ · exp( −4·M·κ·N_S / (N_B+1) )
→ up to a factor-4 improvement in the error EXPONENT
= 6 dB of "quantum advantage", with no change in
transmitted photon number N_S.
This simulator models each trial as a Gaussian discrimination test with this exact exponent scaling: a target is present with 50% probability, the signal photon travels through the noisy region, reflects with probability κ if present, and the receiver decides "present/absent" from a noisy correlation measurement whose effective noise is 4× lower for the quantum (joint-receiver) scheme than for the classical one — reproducing the same asymptotic error rates as the formulas above. Real hardware realises the quantum receiver with an optical parametric amplifier or sum-frequency generation, not a simple correlator; this is a simplified but numerically faithful pedagogical model of that advantage.
- NS — mean signal photon number per pulse (higher = brighter probe, both schemes improve).
- NB — 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 entangled pairs continuously; the 3D scene shows the idler routed straight to the receiver while the signal crosses the noise field, hits the target plane, and returns for the joint measurement.