Quantum Zeno Effect

Frequent Measurement Freezes Quantum Evolution
Survival Probability P(t) with N measurements
P_survival vs Measurement Frequency (at t=1)
Bloch Sphere (qubit state)

Quantum Zeno Effect

A quantum system evolving under H continuously collapses back to its initial state when measured frequently enough.

Survival probability after N measurements in time T: P = [cos²(ΩT/2N)]^N → 1 as N→∞

Key insight: between measurements, P(survive) ≈ 1 − (ΩΔt)². After N measurements: P ≈ [1 − (ΩT/N)²]^N → exp(−Ω²T²/N) → 1

Anti-Zeno effect: some measurement rates accelerate decay.

P(N) = [cos²(ΩT/2N)]^N
N→∞: P→1 (Zeno)
N=1: P=cos²(ΩT/2)