Résumé
We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N - 1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N - 1 contributions. Their modulus is determined by the product of N - 1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N - 1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox (Aharonov and Vaidman 1991 J. Phys. A: Math. Gen. 24 2315-28) from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.
langue originale | Anglais |
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Numéro d'article | 305302 |
Nombre de pages | 26 |
journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 50 |
Numéro de publication | 30 |
Les DOIs | |
Etat de la publication | Publié - 29 juin 2017 |
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Optique, Lasers et spectroscopies
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Thèses de l'étudiant
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A geometric approach to modular and weak values
Auteur: Cormann, M., 7 juil. 2017Superviseur: Caudano, Y. (Promoteur), Hespel, B. (Copromoteur), Lambin, P. (Président), Martin, J. (Personne externe) (Jury) & Matzkin, A. (Personne externe) (Jury)
Student thesis: Doc types › Docteur en Sciences
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