The Zeno effect for coherent states

It is known that by performing dense measurement, that is, by repeating the same measurement a very large number of times in a finite time we can preserve and maintain an initial quantum state. We show here the same effect applying even for the case of the quantum coherent states. Moreover, by taking the complete system of (measured system + measuring system) we prove the Zeno effect not only for the measured system, but also for the complete system. That is, we include here, in our optical treatment of the Zeno effect, the relevant equations of the detecting device, so as to show that the general system (of observed system + observing system) demonstrates the same behaviour under dense measurement as it is regularly demonstrated by the observed system. But unlike the case for noncoherent states where the Zeno effect is proved by applying approximate calculations, here we prove this effect rigorously without any approximation whatsoever. We prove it first for the crosscorrelation case where two points are involved: the point source, and the point of observation where a point detector is located. Then we generalize it to the more realistic case of an extended light source emanating light from more than one spot which is detected by more than one detector.