  We study continuous variable systems, in which quantum and classical degrees
of freedom are combined and treated on the same footing. Thus all systems,
including the inputs or outputs to a channel, may be quantum-classical hybrids.
This allows a unified treatment of a large variety of quantum operations
involving measurements or dependence on classical parameters. The basic
variables are given by canonical operators with scalar commutators. Some
variables may commute with all others and hence generate a classical subsystem.
We systematically study the class of "quasifree" operations, which are
characterized equivalently either by an intertwining condition for phase-space
translations or by the requirement that, in the Heisenberg picture, Weyl
operators are mapped to multiples of Weyl operators. This includes the
well-known Gaussian operations, evolutions with quadratic Hamiltonians, and
"linear Bosonic channels", but allows for much more general kinds of noise. For
example, all states are quasifree. We sketch the analysis of quasifree
preparation, measurement, repeated observation, cloning, teleportation, dense
coding, the setup for the classical limit, and some aspects of irreversible
dynamics, together with the precise salient tradeoffs of uncertainty, error,
and disturbance. Although the spaces of observables and states are infinite
dimensional for every non-trivial system that we consider, we treat the
technicalities related to this in a uniform and conclusive way, providing a
calculus that is both easy to use and fully rigorous.
