Establishing Quantum and Classical Cramer-Rao bounds for estimating the separation between two single molecule dipole emitters

Recently, there have been advancements in the effort to bridge the fields of single molecule super-resolution microscopy and quantum information theory. Utilizing parameter estimation theory, we estimate the separation between two closely spaced single molecule dipole emitters with fixed dipole orientations and quantify precision limits using Quantum Fisher Information and Cramer-Rao bound. Three cases are modeled and compared: the quantum Cramer-Rao bound for a mixed state, classical Cramer-Rao bound for direct imaging, and the classical Cramer-Rao bound utilizing an inversion interferometer. We hope to help improve the field of super-resolution imaging by developing the quantum and classical theories to guide experimental questions such as enhancing localization abilities without a blinking buffer in single molecule experiments.