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Optimal Purity Estimation with Incoherent Measurements
In this work, we consider the fundamental task of estimating the purity of an unknown state to within $\textit{multiplicative}$ error $\varepsilon$. When one can perform general collective measurements, $Θ\left(\frac{\sqrt{d}}{\varepsilon^2} + \frac{d}{\varepsilon}\right)$ copies are known to be nec
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