Covariant measurements and optimality

Abstract

All symmetry groups considered in the previous chapter were parametric groups (Lie groups) of transformations. This means that a parametric set Θ = {θ}, i.e., a continuous manifold in a finite-dimensional space is given and elements of the group G = {g} act as continuous one-to-one mappings of the set Θ onto itself, g : θ → gθ. Moreover the group G is itself parametrized in such a way that the group product g₁g₂ is at least locally continuous in g₁, g₂.