  We review the relationship between positive operator-valued measures (POVMs)
in quantum measurement theory and asymptotic morphisms in the C*-algebra
E-theory of Connes and Higson. The theory of asymptotic spectral measures, as
introduced by Martinez and Trout (CMP 226), is integrally related to positive
asymptotic morphisms on locally compact spaces via an asymptotic Riesz
Representation Theorem. Examples and applications to quantum physics, including
quantum noise models, semiclassical limits, pure spin one-half systems and
quantum information processing will also be discussed.
