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Fidelity Estimation to a Known Quantum State Is Nearly Quadratic in the Smaller Rank
We study the number of copies needed to estimate the root Uhlmann fidelity between an unknown quantum state and a classically known reference, under collective measurements. If the unknown state has rank at most $s$, we give an estimator using $O(s^2/\varepsilon^2)$ copies, uniformly in the ambient
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