This thesis reports on the development of the first quantum enhanced microscope, and on its applications in biological microscopy. The first quantum particle-tracking microscope, described in detail here, represents a pioneering advance in quantum microscopy, which is shown to be a powerful and relevant technique for future applications in science and medicine.
 
The microscope is used to perform the first quantum-enhanced biological measurements -- a central and long-standing goal in the field of quantum measurement. Subdiffraction-limited quantum imaging is achieved, also for the first time, with a scanning probe imaging configuration allowing 10-nanometer resolution.