Weak measurements estimate an operator’s value of a quantum system while minimising the
perturbation of the state, contrary to the usual strong measurement. The observations from
weak measurements with post-selection depend on complex numbers called weak values. When
very large or complex, they are called anomalous weak values and indicate a quantum behaviour.
To get more intuition about their physical meaning, we describe them in the quantum
phase space defined with the Wigner distribution and the Weyl transform. We illustrate the
formalism by a weak measurement of two coupled harmonic oscillators. The weak value is
interpreted as the average value over an interference between pre-selection and post-selection. The particular case of the momentum operator is studied and an interpretation is proposed, using notions from the literature. Then, we transpose the von Neumann model of measurement in phase space for strong and weak post-selected measurements. Using the Stratonovich-Weyl kernel, we then generalise the phase space formalism to curved configuration spaces, useful to describe constrained spaces. The previous results are extended to this situation.
|la date de réponse||22 juin 2022|
|Superviseur||Yves Caudano (Promoteur) & DOMINIQUE LAMBERT (Copromoteur)|
Description of weak measurements and weak values in the phase space representation of quantum mechanics
RENARD, B. (Auteur). 22 juin 2022
Student thesis: Master types › Master en sciences physiques, à finalité spécialisée en physique et data