Quantum algorithm for estimating Renyi entropies of quantum states
Abstract
We describe a quantum algorithm to estimate the alphaRenyi entropy of an unknown ddimensional 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 nonsingular. Our method requires O((da/eps)^2) queries to estimate the alphaRenyi entropy to additive precision 'eps', where 'a' is the dimension of the ancillary register used, assuming the input state is nonsingular. The query complexity of this method is similar to results in the sample complexity model that generally require O((d/eps)^2) samples.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.05251
 Bibcode:
 2019arXiv190805251S
 Keywords:

 Quantum Physics
 EPrint:
 preliminary version, 12 pages