Discrete and continuous measurements

All the examples of measurements so far discussed have in common the fact that the experimental output is either a single number or a finite set of numbers. However, in real measurements the output is often a record of some continuous function of time, from which one can get an understanding of the behavior of the measured quantity during some time interval. This type of measurement is called continuous. Correspondingly, measurements that give a discrete set of numbers can be called discrete.

Let us note that measurements are sometimes called continuous if they are made not instantaneously, but over a finite duration of time. Evidently, this is not a reasonable viewpoint; all real measurements last for a finite time. The dividing line between continuous and discrete measurements is in fact the character of the output signal: does it give information about the measured quantity only at some chosen moment of time, or does it permit a continuous monitoring of the quantity's time evolution.

The necessity to develop the quantum theory of continuous measurements arose in the 1960s, when devices for making continuous measurements were developed with sensitivities close to the quantum level (masers, parametric amplifiers, optical heterodyne receivers, …).