Leggett–Garg Inequality: Testing Macrorealism in Time

The Leggett–Garg inequality is the temporal cousin of Bell's inequality: instead of asking whether two distant particles can share correlations no local hidden-variable theory allows, it asks whether a single system can have a definite, undisturbed value at every moment in time. This simulator precesses a qubit's Bloch vector under a fixed drive and measures a dichotomic observable at three sequential instants t₁, t₂, t₃. Switch between running each pair of measurements as a separate, non-invasive two-time experiment — which lets the Leggett–Garg parameter K climb past the classical bound of 1, up to the quantum maximum of 3/2 — and running all three measurements in a single sequence, where the invasive projective collapse at t₂ forces a classical Markov chain and pins K ≤ 1. A Monte Carlo trial button samples real random outcomes to confirm the analytic prediction empirically.