High School How to teach beginners in quantum theory the POVM concept

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SUMMARY

The discussion centers on teaching the concept of Positive Operator-Valued Measures (POVMs) in quantum theory to beginners. It emphasizes that introducing POVMs is simpler than explaining Born's rule, particularly when starting with qubit states and classical light polarization. The proposed teaching approach includes using the detector response principle (DRP) to derive measurement postulates and employing quantum detection tomography for practical applications. This method provides a more intuitive understanding of quantum measurements compared to traditional methods.

PREREQUISITES
  • Understanding of basic quantum mechanics concepts, including qubits and states.
  • Familiarity with the detector response principle (DRP) in quantum measurements.
  • Knowledge of linear algebra, particularly in relation to Hermitian operators and matrices.
  • Basic grasp of quantum detection tomography and its applications.
NEXT STEPS
  • Study the derivation of the detector response principle (DRP) in quantum measurements.
  • Learn about quantum detection tomography and its role in measuring quantum states.
  • Explore the implications of using Hermitian operators in quantum mechanics.
  • Investigate the relationship between POVMs and Born's rule in quantum theory.
USEFUL FOR

Students and educators in quantum physics, particularly those interested in teaching measurement concepts and quantum theory fundamentals. This discussion is beneficial for anyone looking to simplify complex quantum mechanics topics for beginners.

  • #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
 
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  • #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.
 
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  • #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.
 
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