Bloch sphere representation of three-vertex geometric phases

Details Bloch sphere representation of three-vertex geometric phases Bloch sphere representation of three-vertex geometric phases

2011-07-27

arxiv.org/abs/1107.5447v1

Phys. Rev. A 84, 052114 (2011)

Physics

Quantum Physics

5 pages, 4 figures

Scientific paper

10.1103/PhysRevA.84.052114

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.

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