The exponential modality has been used as a defacto structure for modelling infinite dimensional systems. However, this does not explain what the exponential modalities of linear logic have to do with complementarity. The article uses the formulation of quantum systems within dagger-linear logic and mixed unitary categories, and the formulation of measurement therein to provide a connection. In linear logic the exponential modality has two dual components: it is shown how these components may be compacted into the usual notion of complementarity between two Frobenius algebras on the same object. Thereby exhibiting a complementary system as arising via the compaction of separate systems.