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Quantum Metrology: Beating the Shot-Noise Limit

Interactive Mach-Zehnder interferometer: compare independent (classical) probes, whose phase-estimate noise shrinks as 1/sqrt(N), against entangled/squeezed probes, whose noise shrinks as 1/N — the Heisenberg limit of quantum metrology. Tune probe number N and watch the live estimate histograms.

Physics & Mechanics3DAdvanced60 FPS

This simulator compares two ways of measuring an unknown phase with an interferometer: sending N independent probes one at a time (classical light or uncorrelated atoms), versus sending N probes prepared in an entangled or squeezed quantum state. Independent probes average down their noise only as 1/√N — the standard quantum limit. Entangled probes exploit quantum correlations to average down as 1/N — the Heisenberg limit. Tune the number of probes and watch the two live histograms of repeated phase estimates converge on the true value at very different rates.

⚙ Under the hood

Interactive Mach-Zehnder interferometer comparing classical (independent) probes, whose phase-estimate noise falls as 1/sqrt(N), against entangled/squeezed probes, whose noise falls as 1/N — the Heisenberg limit of quantum metrology. Tune probe number N and watch live estimate histograms converge on the true phase.

quantum metrologysqueezed lightentanglementshot noiseHeisenberg limitinterferometerprecision measurement

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install