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Optimal single-copy estimation of quantum state moments: why $\operatorname{Tr}(ρ^3)$ and $\operatorname{Tr}(ρ^4)$ are equally hard
Estimating nonlinear properties of an unknown quantum state with restrictive experimental accessibility is a fundamental problem in quantum learning. We study the sample complexity of estimating the state moments $\operatorname{Tr}(ρ^t)$, allowing arbitrary adaptive single-copy measurements. While p
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