Quantum algorithm for estimating α -Renyi entropies of quantum states
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Abstract
We describe a quantum algorithm to estimate the alpha-Renyi entropy of an unknown d-dimensional density matrix, for alpha not equal to 1, by combining the recent technique of quantum singular value transformations with the method of estimating normalised traces in the one clean qubit model. We consider the purified oracular input model where the input state is prepared via a quantum oracle that outputs a purified version of the state, assumed to be non-singular. Our method requires O((da/eps)^2) queries to estimate the alpha-Renyi entropy to additive precision 'eps', where 'a' is the dimension of the ancillary register used, assuming the input state is non-singular. The query complexity of this method is similar to results in the sample complexity model that generally require O((d/eps)^2) samples.