Utilizing quantum properties of light to break the diffraction limit has been the goal of intense research in the recent years. This paper is a progress report on a study aimed at experimentally demonstrating a superresolution microscopy technique enabled by photon antibunching, a non-classical emission statistics feature exhibited by most emitters used as fluorescent markers. We find that photon antibunching gives rise to correlations that encode high spatial frequency information on the distribution of fluorescent emitters. Detecting these correlations using photon counting instrumentation in a standard fluorescence microscope setting allows for three-dimensional superresolution imaging of fluorophore stained samples. The technique provides a quantum alternative to the established superresolution tools.