تقرير
Teaching ideal quantum measurement, from dynamics to interpretation
| العنوان: | Teaching ideal quantum measurement, from dynamics to interpretation |
|---|---|
| المؤلفون: | Allahverdyan, Armen E., Balian, Roger, Nieuwenhuizen, Theo M. |
| المصدر: | Comptes Rendus. Physique, Volume 25 (2024), pp. 251-287 |
| سنة النشر: | 2024 |
| المجموعة: | Condensed Matter High Energy Physics - Theory Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Condensed Matter - Mesoscale and Nanoscale Physics, High Energy Physics - Theory |
| الوصف: | We present a graduate course on ideal measurements, analyzed as dynamical processes of interaction between the tested system S and an apparatus A, described by quantum statistical mechanics. The apparatus A=M+B involves a macroscopic measuring device M and a bath B. The requirements for ideality of the measurement allow us to specify the Hamiltonian of the isolated compound system S+M+B. The resulting dynamical equations may be solved for simple models. Conservation laws are shown to entail two independent relaxation mechanisms: truncation and registration. Approximations, justified by the large size of M and of B, are needed. The final density matrix $\hat{\cal D}(t_f)$ of S+A has an equilibrium form. It describes globally the outcome of a large set of runs of the measurement. The measurement problem, i.e., extracting physical properties of individual runs from $\hat{\cal D}(t_f)$, then arises due to the ambiguity of its splitting into parts associated with subsets of runs. To deal with this ambiguity, we postulate that each run ends up with a distinct pointer value $A_i$ of the macroscopic M. This is compatible with the principles of quantum mechanics. Born's rule then arises from the conservation law for the tested observable; it expresses the frequency of occurrence of the final indications $A_i$ of M in terms of the initial state of S. Von Neumann's reduction amounts to updating of information due to selection of $A_i$. We advocate the terms $q$-probabilities and $q$-correlations when analyzing measurements of non-commuting observables. These ideas may be adapted to different types of courses. Comment: 32 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.20353 |
| رقم الأكسشن: | edsarx.2405.20353 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |