Bloch sphere representation of three-vertex geometric phases

Abstract

The properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three quantum states in an N-state quantum system can be represented by N-1 spherical triangles on the Bloch sphere. The parameter dependence of the geometric phase was analyzed based on this picture. We found that the geometric phase exhibits rich nonlinear behavior in a high-dimensional Hilbert space.

5 pages, 4 figures

References in corpus (7)

• Experimental Realization of Polarization Qutrits from Non-Maximally Entangled States
• Geometrical aspects of weak measurements and quantum erasers
• Complete solution for unambiguous discrimination of three pure states with real inner products
• Bi-directional mapping between polarization and spatially encoded photonic qutrits
• Direct observation of geometric phases using a three-pinhole interferometer
• Observation of geometric phases in quantum erasers
• Nonlinear behavior of geometric phases induced by photon pairs

Cited by in corpus (10)

• Modal Majorana sphere and hidden symmetries of structured-Gaussian beams
• Anticoherence measures for pure spin states
• Geometric description of modular and weak values in discrete quantum systems using the Majorana representation
• The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
• Observation of nonlinear variations in three-vertex geometric phase in two-photon polarization qutrit
• Coherent-State Approach for Majorana representation
• Berry phases of higher spins due to internal geometry of Majorana constellation and relation to quantum entanglement
• Geometric decomposition of geodesics and null phase curves using Majorana star representation
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation