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

量子费雪信息 (QFI) 在量子信息理论和许多实际应用（如量子计量学）中起着至关重要的作用。然而，计算 QFI 通常是一项计算要求高的任务。在这项工作中，我们分析了 QFI 的下限，我们称之为子量子费雪信息 (sub-QFI)。可以在量子计算机上使用 2 n有效地估计n个量子位状态的界限量子位。次级 QFI 基于超保真度，即乌尔曼保真度的上限。我们在单一族的背景下分析次级 QFI，在那里我们推导出几个关键属性，包括其几何解释。特别是，我们证明 QFI 和 sub-QFI 在相同的最佳状态下最大化，这意味着 sub-QFI 忠实于 QFI，因为这两个数量共享相同的全局极值。基于这种忠实性，子 QFI 充当 QFI 的有效可计算替代品，用于量子传感和量子计量应用。最后，我们为 sub-QFI 提供了额外的含义，作为一致性、不对称性和纯度损失的衡量标准。