Quantum Zeno Effect

Frequent measurements freeze quantum evolution — the watched pot never boils. For N measurements in time T, survival probability P(T) → 1 as N → ∞, since each measurement collapses the state back to |0⟩.

Parameters

Rabi oscillation:
P(t) = cos²(Ωt/2)

With N measurements at t_k=kT/N:
P_N(T) = [cos²(ΩT/2N)]^N

As N→∞: P_N(T) → 1
(Zeno limit)

Green: free evolution
Orange: with N measurements
Blue dots: measurement outcomes

T=π/Ω = full inversion (P=0)
P_N(T) =
P_free(T) =