Abstract
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.
Original language | English |
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Article number | 305302 |
Number of pages | 26 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 50 |
Issue number | 30 |
DOIs | |
Publication status | Published - 29 Jun 2017 |
Keywords
- geometric phase
- Majorana representation
- modular value
- three-box paradox
- weak measurement
- Weak value
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Optics, Lasers and spectroscopy
Muriel Lepere (Manager)
Technological Platform Optics, Lasers and spectroscopyFacility/equipment: Technological Platform
Student theses
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A geometric approach to modular and weak values
Author: Cormann, M., 7 Jul 2017Supervisor: Caudano, Y. (Supervisor), Hespel, B. (Co-Supervisor), Lambin, P. (President), Martin, J. (External person) (Jury) & Matzkin, A. (External person) (Jury)
Student thesis: Doc types › Doctor of Sciences
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