Quantum illumination (Lloyd, Science 2008; Tan et al., PRL 2008) generates entangled signal/idler photon pairs, sends the signal to probe a region that may hold a very weak reflector (reflectivity η) sitting in bright thermal background noise (mean NB photons/mode), and keeps the idler locally. A joint receiver correlates the returning signal against the stored idler, rather than measuring signal power alone.
Remarkably, the entanglement itself does not survive the lossy, noisy round trip — yet residual photon-number correlations let the optimal joint (quantum) receiver beat the best possible classical coherent-state receiver of equal transmitted energy. For binary hypothesis testing (target present vs absent) over M pulses, the Chernoff-bound error probability is:
P_e(M) ≈ (1/4) · exp(-M·κ)
This simulator uses a closed-form model that reproduces the literature's qualitative scaling — a factor-of-4 (6 dB) exponent gain in the photon-starved, noise-dominated regime (NS ≪ 1, NB ≫ 1), vanishing as the signal gets brighter or the background gets quieter:
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)
- η, NB, NS — set the target's weakness, the background clutter level, and how bright the illuminating pulses are.
- M — how many pulses the receiver integrates before deciding; Pe falls exponentially with M for both receivers, but faster for the quantum one.
- Quantum vs Classical — selects which κ and Pe are reported as the "active mode" headline numbers.
- The 3D scene and the two live bars are an illustrative Monte-Carlo receiver: every pulse, a genuine target return is weighted fully, while an uncorrelated clutter click is weighted fully for the classical (counting) receiver but suppressed toward zero for the quantum (idler-correlated) receiver — visualising why joint detection rejects noise that plain photon counting cannot.
Real-world relevance: this is the mechanism behind proposed quantum radar and LIDAR schemes for detecting faint, low-reflectivity objects in bright thermal or jamming backgrounds, and behind entanglement-enhanced target discrimination research at microwave and optical frequencies.