Generalized measure of quantum Fisher information

Here, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI measure. Specifically, it is essentially a QFI measure for subnormalized states, and hence it generalizes the standard QFI in this sense. Our bound employs the generalized fidelity applied to a truncated state, which is constructed via the m largest eigenvalues and their corresponding eigenvectors of the probe quantum state ρθ. Focusing on unitary families of exact states, we analyze the properties of our proposed lower bound, and demonstrate its utility for efficiently estimating the QFI.