B How to teach beginners in quantum theory the POVM concept

Click For Summary
The discussion emphasizes the advantages of teaching the Positive Operator-Valued Measure (POVM) concept in quantum theory to beginners, arguing it is more intuitive and simpler than introducing Born's rule. The approach suggested involves starting with qubits and using classical light polarization to motivate the concept of measurement. The derivation of the POVM from basic principles, such as the detector response principle, is highlighted as straightforward and provides a solid foundation for understanding quantum measurements. The conversation also touches on the necessity of introducing infinite-dimensional Hilbert spaces for more complex systems, such as the anharmonic oscillator, and the importance of relating quantum mechanics to classical mechanics. Overall, the POVM framework is presented as a more accessible entry point into quantum theory for students.
  • #61
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
 
Physics news on Phys.org
  • #62
vanhees71 said:
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.
 
  • Like
Likes vanhees71
  • #63
vanhees71 said:
At least it's about the right topic and also discusses the SGE in some detail.
Here is another book of interest:
Chapter 7 discusses a number of realistic examples. In the introduction to the chapter (p.258 of the online version) he writes:

Willem de Muynck said:
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.
 
Last edited:
  • Like
Likes Demystifier and vanhees71

Similar threads

  • · Replies 35 ·
2
Replies
35
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 18 ·
Replies
18
Views
3K
  • · Replies 2 ·
Replies
2
Views
11K
  • · Replies 0 ·
Replies
0
Views
1K
  • · Replies 75 ·
3
Replies
75
Views
10K
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
2K