  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.
