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