Sub-quantum Fisher information

The quantum Fisher information (QFI) plays a crucial role in theory and many practical applications such as metrology. However, computing the QFI is generally computationally demanding task. In this work we analyze lower bound on which call sub-quantum (sub-QFI). can be efficiently estimated computer for an n-qubit state using 2n qubits. sub-QFI based super-fidelity, upper Uhlmann's fidelity. We context of unitary families, where derive several properties including its geometrical interpretation. particular, prove that are maximized same optimal state, implies faithful to sense both quantities share global extrema. Based faithfulness, acts computable surrogate sensing metrology applications. Finally, provide additional meaning measure coherence, asymmetry, purity loss.