Continuous measurement

Vladimir B. Braginsky, Farid Ya Khalili, Kip S. Thorne

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, …).

Alberto Barchielli, Matteo Gregoratti

Miklós Rédei, A. Zartl, Erwin Schrödinger +9 more

Michael B. Mensky

This chapter explores accurate formulation of the approach, including a description of the evolution of the measured system and the generalized unitarity condition for this evolution. It argues that evolution under continuous measurement has both quantum and classical features. The chapter deals with the evolution of the system subject to continuous measurement. It demonstrates in general form and considers the specific example of a free particle scattered because its position is measured. The quantum theory of measurements has been discussed not only because of its conceptual interest but also for practical purposes. The chapter discusses the application of the measurement amplitude for estimation of probabilities of different measurement outputs. However, the same amplitude can be used to describe the evolution of the system subject to the measurement. The chapter shows the continuous measurement changes the evolution of the quantum system undergoing the measurement.

Lajos Diósi

We have proposed a formal theory for the continuous measurement of relativistic quantum fields. We have also derived the corresponding scattering equations. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of our theory. A possible example of the relativistic continuous measurement has been outlined in standard quantum electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields.

Stanley Gudder