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.
|Number of pages||26|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 29 Jun 2017|
- geometric phase
- Majorana representation
- modular value
- three-box paradox
- weak measurement
- Weak value
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Muriel Lepere (Manager)Technological Platform Optics, Lasers and spectroscopy
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