Bloch sphere representation of three-vertex geometric phases

TL;DR

This paper explores the geometric phases among three quantum states in high-dimensional systems using the Majorana representation, revealing their representation as spherical triangles on the Bloch sphere and uncovering complex nonlinear behaviors.

Contribution

It introduces a novel geometric interpretation of three-vertex phases in high-dimensional quantum systems via the Majorana representation.

Findings

Geometric phases can be represented by N-1 spherical triangles on the Bloch sphere.

The geometric phase shows rich nonlinear dependence on parameters.

The approach provides new insights into high-dimensional quantum state geometry.

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.