Generating function and Bloch representation for quantum Fisher tensor
The paper shows that logarithms of Uhlmann relative amplitude between density matrices act as generating functions for key quantum metrological quantities like the quantum Fisher tensor and mean Uhlmann curvature. It derives a generic expression for these tensors using the Bloch representation of density matrices, which allows calculation in arbitrary dimensions. In the pure state limit, this formalism recovers known geometric concepts like the quantum geometric tensor.