Abstract
Following the introduction and study of a range of concrete operator measures representing quantum mechanical observables in earlier chapters (notably Chaps. 8, 14–17), we now apply the tools of measurement theory developed in Chap. 10 to illustrate the implementation of more or less realistic measurement schemes for typical observables.
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Notes
- 1.
The coupling operator used by Arthurs and Kelly has \(P_2\) in the place of \(Q_2\), so that in this case the appropriate pointer observable for the second probe is \(Q_2\).
- 2.
- 3.
A rigorous proof of this equation is obtained by adaptation of arguments from [5] along the lines of Exercises 6, 7 and 8 of Chap. 15. This also shows that (19.1) defines a unitary operator, without giving explicitly the spectral decomposition of the unique selfadjoint extension of the essentially selfadjoint operator \(-\lambda Q\otimes P_1\otimes I_2\,+\kappa \, P\otimes I_1\otimes Q_2\).
- 4.
This presentation follows closely [13].
- 5.
The development of the examples in this section follows closely the review [24].
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Busch, P., Lahti, P., Pellonpää, JP., Ylinen, K. (2016). Measurement Implementations. In: Quantum Measurement. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-43389-9_19
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