Real quantum measurements
The modelization of measurement systems must take into account the fluctuations with a fundamental origin as well as the imperfections of the experimental setup (realistic description réaliste of the measurement apparatus).
A treatment of this problem based on quantum network theory allows one to account for thermal noise (coupling with the environment), quantum noise (quantum nature of the measurement process), amplification noise (active systems for signal amplification or feedback loops), the finite duration of the measurement.
Amplifiers play a crucial role in ultrasensitive measurement setups. They bring the signal from the microscopic level to an observable macroscopic level. They are also used to keep the apparatus at its optimal working point thanks to feedback loops. The treatment by quantum network theory allows one to describe the role of these active elements.
An electrical system often used is the operational amplifier. It is possible to model ultimate quantum fluctuations of this system by two noise sources, a current and a tension which do not commute with each other. This simple representation may then be used to describe more elaborate quantum networks containing active elements.
A review paper on these topics :
Thermal and quantum noise in active systems, Courty J.-M., Grassia F., Reynaud S., in Noise, Oscillators and Algebraic Randomness (Lecture Notes in Physics, 71, Springer, 2000) HAL