  A unification of the set of quasiprobability representations using the
mathematical theory of frames was recently developed for quantum systems with
finite-dimensional Hilbert spaces, in which it was proven that such
representations require negative probability in either the states or the
effects. In this article we extend those results to Hilbert spaces of infinite
dimension, for which the celebrated Wigner function is a special case. Hence,
this article presents a unified framework for describing the set of possible
quasiprobability representations of quantum theory, and a proof that the
presence of negativity is a necessary feature of such representations.
