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 -state quantum system can be represented by 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.
- Received 27 July 2011
DOI:https://doi.org/10.1103/PhysRevA.84.052114
©2011 American Physical Society