Ramsey Fringe & Estimation Convergence: SQL vs Heisenberg Limit

This simulator is the 2D counterpart to the 3D quantum-metrology sim, and it visualizes the same physics through the two plots a real metrologist reads instead of a 3D scene of orbiting atoms. The top panel draws the Ramsey fringe — click probability versus the unknown phase — for both regimes at once, in phase units normalized so N cancels out of the GHZ curve entirely: switch modes and watch the effective fringe go from a broad, shallow SQL curve to a GHZ curve that completes a full oscillation across the same range, exactly N times narrower. Real binomial Monte Carlo outcomes land on the active curve shot by shot, and two markers track the true (hidden) phase against the running maximum-likelihood estimate as it locks on. The bottom panel turns that convergence into a live decades-of-precision chart, −log₁₀ of the estimation error, so the 1/√(N·m) shot-noise floor and the entangled 1/(N·√m) Heisenberg floor are visible as literal shrinking distance to the top of the chart rather than as abstract formulas.