Uncertainty Relations for Metrology and Computation

Abstract: Uncertainty relations are a familiar part of any introductory quantum mechanics course. In this talk, I will summarize how uncertainty relations have been re-interpreted and re-expressed in the language of information theory, leading to connections with the geometry of quantum state space and the limits of computational and information processing efficiency. As two particular examples, I will discuss how uncertainty relations allow one to design information-theoretically optimal measurement protocols for function estimation in networks of quantum sensors and how they enable one to bound the speed at which analog quantum computers can possibly perform optimization tasks.