Author

G. Lee

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Preprint Aug 2026

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 dimension and refere...

G. Lee, Sunghyeon Jo · 0 citations

Preprint Aug 2026

The Sample Complexity of Fidelity Estimation to a Known Rank-$r$ Reference State Is $\widetilde{\Theta}(r^2/\varepsilon^2)$

We settle the sample complexity of estimating the root Uhlmann fidelity $F(\rho,\sigma)=\operatorname{tr}\sqrt{\sqrt{\sigma}\rho\sqrt{\sigma}}$ between an unknown state $\rho$ and a known rank-$r$ reference state $\sigma$. Writing $S(r,\varepsilon)$ for the sample complexity at additive error $\varepsilon$, we resolve...

G. Lee, Sunghyeon Jo · 0 citations