  Recently, it was discovered that the `quantum partial information' needed to
merge one party's state with another party's state is given by the conditional
entropy, which can be negative [Horodecki, Oppenheim, and Winter, Nature 436,
673 (2005)]. Here we find a classical analogue of this, based on a long known
relationship between entanglement and shared private correlations: namely, we
consider a private distribution held between two parties, and correlated to a
reference system, and ask how much secret communication is needed for one party
to send her distribution to the other. We give optimal protocols for this task,
and find that private information can be negative - the sender's distribution
can be transferred and the potential to send future distributions in secret is
gained through the distillation of a secret key. An analogue of `quantum state
exchange' is also discussed and one finds cases where exchanging a distribution
costs less than for one party to send it. The results give new classical
protocols, and also clarify the various relationships between entanglement and
privacy.
