Abstract

The conventional description of a measurement is expressed in terms of the eigenstates of an Hermitian operator representing the observed quantity or ‘observable’. Most real measurements do not fit into this simple description, however, and it is necessary to have a more general theoretical framework to describe these. Closer investigation reveals that the best measurement we can perform in any given situation is usually of this more general form. A striking example is the possibility of discriminating without error between two non-orthogonal polarization states of a single photon. I shall demonstrate how this and other optimal decision-making strategies have been found and illustrate these ideas by reference to experiments.