Fidelity estimation to a known rank-r reference state requires Theta-tilde(r^2/epsilon^2) copies, closing the factor-r gap between known upper and lower bounds.
Ledoux,The Concentration of Measure Phenomenon, American Mathematical Society, 2001
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The Sample Complexity of Fidelity Estimation to a Known Rank-$r$ Reference State Is $\widetilde{\Theta}(r^2/\varepsilon^2)$
Fidelity estimation to a known rank-r reference state requires Theta-tilde(r^2/epsilon^2) copies, closing the factor-r gap between known upper and lower bounds.