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Mathematical foundation of the U N ( 1 ) quantum geometric tensor
Xin Wang1, Xu-Yang Hou1, Jia-Chen Tang1
1School of Physics, Southeast University, Nanjing 211189, China.
Abstract:
In this paper, we systematically establish the mathematical foundation for the quantum geometric tensor (QGT) of mixed states Explicitly, we present a description based on the principal bundle and derive a Pythagorean-like distance decomposition equation. Additionally, we offer a comprehensive comparison of its properties with those of the U(1) principal bundle description of the pure-state QGT. Finally, we prove a fundamental inequality for the QGT and discuss its physical implication.
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