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Quantum Fisher information measures the local statistical distinguishability of neighboring states. Braunstein and Caves derived the quantum statistical metric by optimizing distinguishability over measurements [ 9 ] . For a single parameter $\theta$ and $\nu$ independent repetitions, the quantum Cramér–Rao relation is commonly written $\operatorname{Var}(\hat\theta)\geq \frac{1}{\nu F_Q(\theta)}$. under the relevant regularity and unbiasedness conditions. The variance has squared-coordinate units, so $F_Q$ has inverse-squared-coordinate units. Paris’s review emphasizes that quantum estimation is an optimization problem over measurements and explains the symmetric-logarithmic-derivative construction used to calculate the bound [ 10 ] .

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