Teaching POVM through detector response and Born's rule

[vanhees71]

Seems to be a great book! I've even (legal) access to it, though it's published in 1995. Is this the book you have in mind? At least it's about the right topic and also discusses the SGE in some detail.

https://rd.springer.com/book/10.1007/978-3-540-49239-9

 

[A. Neumaier]

Seems to be a great book! I've even (legal) access to it, though it's published in 1995. Is this the book you have in mind? At least it's about the right topic and also discusses the SGE in some detail.

https://rd.springer.com/book/10.1007/978-3-540-49239-9

Yes, this is the book I had quoted from. There is also another, quite recent book with two authors the same:

• P. Busch, P. Lahti, J. Pellonpää and K. Ylinen, Quantum Measurement, Springer, Berlin 2016.

with a number of chapters on realistic POVM measurements, but the other book is much more elementary.

 

[A. Neumaier]

At least it's about the right topic and also discusses the SGE in some detail.

Here is another book of interest:

• W.M. de Muynck, Foundations of Quantum Mechanics, an Empiricist Approach, Kluwer, Dordrecht 2002. (note: the online copy linked to is slightly different from the published version)

Chapter 7 discusses a number of realistic examples. In the introduction to the chapter (p.258 of the online version) he writes:

The examples discussed in sections 7.2 through 7.5 show that a generalization of the formalism is necessary for describing even the most common methods of quantum mechanical measurement, like the detection of photons using a detector that is not 100% efficient. This also holds true for such experiments as the double slit experiment, being a paradigm of standard quantum mechanics. It will not be surprising, then, that an analysis of this experiment based on the standard formalism can hardly be a reliable one, and that conclusions based on such an analysis should be considered with some reservation.

With ''generalization of the formalism'' he means the POVM formalism generalizing the traditional textbook formalism which only features projective measurements.