Michael Grace, University of Arizona
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Abstract: We humans observe the world around us every day, but how efficiently do we make use of the sensory input we receive? In high-resolution optical imaging contexts, extracting the maximum possible amount of information from each photon that is collected by a telescope or microscope is of paramount importance. Estimation theory is frequently employed to quantify the expected performance of data-acquisition and -processing schemes for quantitative tasks of inference, such as parameter estimation and hypothesis testing. For systems which can be described by quantum mechanics, such as incoherent light from stars or fluorescent proteins, quantum estimation theory equips us with even more powerful tools to readily calculate ultimate, task-specific performance bounds which are automatically optimized over all experimental protocols, all physical sensors, and all post-processing algorithms allowed by the laws of physics. Such “quantum limits” have recently been calculated for standard high-resolution imaging tasks, leading to the surprising result that historical resolution limits based on the optical principle of diffraction are artifacts arising from the detection of light in a sub-optimal measurement basis. In this seminar, I will overview these recent theoretical results and describe my ongoing research on a multi-parameter estimation framework for sub-diffraction optical imaging with limited or nonexistent prior information. In particular, I will motivate and derive a quantum estimation limit I have developed called the Marginal Quantum Cramér-Rao Bound, which gives an ultimate variance bound for parameter estimation in the presence of unknown nuisance parameters.