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Article Dans Une Revue Comptes Rendus. Physique Année : 2024

Teaching ideal quantum measurement, from dynamics to interpretation

Enseigner les mesures quantiques idéales, de la dynamique à l'interprétation

Résumé

We present a graduate course on ideal measurements, analyzed as dynamical processes of 14 interaction between the tested system S and an apparatus A, described by quantum statistical 15 mechanics. The apparatus A=M+B involves a macroscopic measuring device M and a bath B. 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 19 and registration. Approximations, justified by the large size of M and of B, are needed. The final density matrix Dˆ 20 ($t_f$) of S+A has an equilibrium form. It describes globally the outcome 21 of a large set of runs of the measurement. The measurement problem, i.e., extracting physical properties of individual runs from Dˆ 22 ($t_f$), 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 Ai 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 26 observable ; it expresses the frequency of occurrence of the final indications Ai of M in terms of the initial state of S. Von Neumann’s reduction amounts to updating of information due to selection of Ai . 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.
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cea-04544555 , version 1 (22-04-2024)

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  • HAL Id : cea-04544555 , version 1

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Armen E Allahverdyan, Roger Balian, Theodorus M. Nieuwenhuizen. Teaching ideal quantum measurement, from dynamics to interpretation. Comptes Rendus. Physique, In press. ⟨cea-04544555⟩
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