Evaluation of quantum Fisher information for large system

Abstract: Quantum Fisher information (QFI) plays a vital role in quantum precision measurement, quantum information, many-body physics, and other domains. Obtaining the QFI from experiment for a quantum state reveals insights such as the limits of estimation accuracy for a certain parameter, the degree of entanglement, and the geometric characteristics of the quantum state. Nonetheless, the measurement complexity of the QFI and its lower bound hinges on the dimension of the quantum state. Consequently, reducing the complexity of measurement is a significant challenge. This paper presents a methodology for evaluating the QFI of high-dimensional systems by transferring information to an auxiliary system and measuring its sub-QFI, while also offering conditions to diminish the dimension of auxiliary system to be measured without affecting the amount of information obtained by it.