  We show that no entanglement is necessary to distribute entanglement; that
is, two distant particles can be entangled by sending a third particle that is
never entangled with the other two. Similarly, two particles can become
entangled by continuous interaction with a highly mixed mediating particle that
never itself becomes entangled. We also consider analogous properties of
completely positive maps, in which the composition of two separable maps can
create entanglement.
