Quantum Zeno Effect — Measurement-Induced Freezing

Quantum Zeno effect (Misra & Sudarshan 1977): Frequent measurement of a quantum system inhibits its decay. For a two-level system |↑⟩→|↓⟩, the survival probability after a single free evolution step τ_m is P(τ_m) ≈ 1 − Ω²τ_m². After n = T/τ_m measurements: P(T) = [1 − Ω²τ_m²]^{T/τ_m} ≈ exp(−Ω²τ_m·T) → 1 as τ_m→0. Anti-Zeno effect: At intermediate measurement rates matching the bath spectral density, decay is accelerated. The effective decay rate Γ_eff(τ_m) = −ln[P(τ_m)]/τ_m passes through a minimum (Zeno) and maximum (anti-Zeno) as a function of 1/τ_m. With dissipation γ, the short-time survival is P(τ) ≈ exp(−γτ − Ω²τ²), giving Γ_eff ≈ γ + Ω²τ_m for small τ_m.