A DQC1-based algorithm estimates α-Rényi entropies of non-singular quantum states to additive or multiplicative precision using purified access, at expected cost O(1/(xε)^2) measurements.
Kim, Low complexity estimation method of rényi entropy for ergodic sources, Entropy 20, 657 (2018)
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Quantum algorithm for estimating Renyi entropies of quantum states
A DQC1-based algorithm estimates α-Rényi entropies of non-singular quantum states to additive or multiplicative precision using purified access, at expected cost O(1/(xε)^2) measurements.