  Here it is shown that the squashed entanglement has an operational meaning --
it is the fastest rate at which a quantum state can be sent between two parties
who share arbitrary side-information. Likewise, the entanglement of formation
and entanglement cost is shown to be the fastest rate at which a quantum state
can be sent when the parties have access to side-information which is maximally
correlated. A further restriction on the type of side-information implies that
the rate of state transmission is given by the quantum mutual information. This
suggests a new paradigm for understanding entanglement and other correlations.
Different types of side-information correspond to different types of
correlations with the squashed entanglement being one extreme. The paradigm
also allows one to classify states not only in terms of how much quantum
communication is needed to transfer half of it, but also in terms of how much
entanglement is needed. Furthermore, there is a dual paradigm: if one
distributes the side-information as maliciously as possible so as to make the
sending of the state as difficult as possible, one finds maximum rates which
give interpretations to known quantities (such as the entanglement of
assistance), as well as new ones. The infamous additivity questions can also be
recast and receive an operational interpretation in terms of maximally
correlated states.
