Majorana’s stellar representation for the quantum geometric tensor of symmetric states

Abstract

Majorana’s stellar representation provides an intuitive picture in which quantum states in high-dimensional Hilbert space can be observed using the trajectory of Majorana stars. We consider the Majorana’s stellar representation of the quantum geometric tensor for a spin state up to spin-3/2. The real and imaginary parts of the quantum geometric tensor, corresponding to the quantum metric tensor and Berry curvature, are therefore obtained in terms of the Majorana stars. Moreover, we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases. Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana’s stars.