<i>Colloquium</i>: Incompatible measurements in quantum information science

Abstract

It is common to say that a quantum measurement is described by a Hermitian operator; e.g., we do a ``position'' measurement or a ``momentum'' measurement. The modern perspective is that this is too narrow a view of what a measurement can be, with more concepts needed, like partial measurement, weak measurement, and a quantum instrument. This Colloquium provides a larger perspective, and shows how measurement incompatibility and related uncertainty relations are extended to more general settings. One such insight is that measurements that disturb each other are in fact a valuable resource in a variety of quantum information protocols.