Optimal Measurement Protocols in Quantum Zeno Effect

Abstract: The quantum Zeno effect is the prediction, going back to Alan Turing, that the decay of an unstable system can be slowed down by measuring it frequently enough. It was also noticed later that the opposite effect, i.e., enhancement of the decay due to frequent measurements, is rather common. An important question arising in this regards is how to choose the optimal measurement strategy to achieve the highest possible decay rate. Here we rigorously prove the universal optimality of the stroboscopic measurement protocol in the sense that it always provides the shortest expected decay time among all measurement procedures. However, the implementation of the stroboscopic protocol requires the knowledge of the optimal sampling period which may depend on the fine details of the quantum problem. We show that this difficulty can be overcame with the simple non-regular measurement procedures inspired by the scale-free restart strategies used to speed up the completion of random search tasks and probabilistic algorithms in computer science. Besides, our analysis reveals the universal criteria to discriminate between Zeno and anti-Zeno regimes for the unstable quantum systems under Poissonian measurements.