Limitations in quantum metrology approaches to imaging resolution

Can a quantum advantage for imaging resolution be realized with the help of quantum estimation theory? We expect so, but we show that, presently, theoretical tools are insufficiently developed to answer this question for extended objects. Still, there is much to be learned from the current state of the art. In this review, we re-examine prominent results in the literature and probe the limits of quantum metrology in addressing imaging resolution. In particular, we show that under restrictive but well-defined conditions, any quantum advantage in one-dimensional phase imaging appears to diminish for increasingly detailed objects. We also show that a previous attempt at tackling this question, while incomplete, does predict an advantage for single-molecule localization microscopy, although this method may not be feasible in the near term. As for experimental claims of Heisenberg-limited imaging resolution, we briefly address the many inherent difficulties in demonstrating that such a thing has indeed been achieved.This article is part of the theme issue 'The quantum theory of light'.