  Quantum Fisher information (QFI) is a central concept in quantum sciences
used to quantify the ultimate precision limit of parameter estimation, detect
quantum phase transitions, witness genuine multipartite entanglement, or probe
nonlocality. Despite this widespread range of applications, computing the QFI
value of quantum many-body systems is, in general, a very demanding task. Here
we combine ideas from functional theories and quantum information to develop a
novel functional framework for the QFI of fermionic and bosonic ground states.
By relying upon the constrained-search approach, we demonstrate that the QFI
matricial values can universally be determined by the one-body reduced density
matrix (1-RDM), avoiding thus the use of exponentially large wave functions.
Furthermore, we show that QFI functionals can be determined from the universal
1-RDM functional by calculating its derivatives with respect to the coupling
strengths, becoming thus the generating functional of the QFI. We showcase our
approach with the Bose-Hubbard model and present exact analytical and numerical
QFI functionals. Our results provide the first connection between the one-body
reduced density matrix functional theory and the quantum Fisher information.
