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Simultaneous Estimation of Nonlinear Functionals of a Quantum State
We consider a fundamental task in quantum information theory, estimating the values of $tr(Oρ)$, $tr(Oρ^2)$, $\ldots$, $tr(Oρ^k)$ for an observable $O$ and a quantum state $ρ$. We show that $\widetildeΘ(k)$ samples of $ρ$ are sufficient and necessary to simultaneously estimate all the $k$ values. Th
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