Evaluation of the quantum Fisher information for large systems via an ancilla

Quantum Fisher information (QFI) is a fundamental quantity in quantum information and quantum mechanics, and evaluating it in various physical systems has become an important research topic. However, its evaluation in large systems still faces many challenges. Hereby we propose an ancilla-based protocol for evaluating the QFI of large systems and establish the conditions under which this protocol can ``perfectly'' evaluate the QFI in theory. As a demonstration, the protocol is applied to quantum circuits to evaluate the QFI of the Greenberger-Horne-Zeilinger state.