Distributional property testing in a quantum world

@inproceedings{Gilyn2020DistributionalPT,
  title={Distributional property testing in a quantum world},
  author={Andr{\'a}s Gily{\'e}n and Tongyang Li},
  booktitle={ITCS},
  year={2020}
}
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing closeness between unknown distributions, testing independence between two distributions, and estimating the Shannon / von Neumann entropy of distributions. The distributions can be either classical or quantum, however our quantum algorithms require coherent… 
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