Quantum anti-zeno paradox

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator E(t) = U(t)EUdagger(t) is measured continuously from t = 0 to T, where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If U(t) not equal1, the watched kettle is sure to "boil."