Quantum Zeno Effect in Heisenberg Picture and Critical Measurement Time

Quantum Zeno effect is conventionally interpreted by the assumption of the wave-packet collapse, in which does not involve the duration of measurement. However, we predict duration \(\tau_m\) of each measurement will appear in quantum Zeno effect by a dynamical approach. Moreover, there exists a model-free critical measurement time, which quantum Zeno effect does not occur when \(\tau_m\) takes some special values. In order to give these predictions, we first present a description of quantum Zeno effect in the Heisenberg picture, which is based on the expectation value of an observable and its fluctuation. Then we present a general proof for quantum Zeno effect in the Heisenberg picture, which is independent of the concrete systems. Finally, we calculate the average population and relative fluctuation after \(N\) successive measurements in XX model, which agrees with our prediction about the critical measurement time.