  The polarization phenomenon for a single source is extended to a framework
with multiple correlated sources. It is shown in addition to extracting the
randomness of the source, the polar transforms takes the original arbitrary
dependencies to extremal dependencies. Polar coding schemes for the
Slepian-Wolf problem and for secret key generations are then proposed based on
this phenomenon. In particular, constructions of secret keys achieving the
secrecy capacity and compression schemes achieving the Slepian-Wolf capacity
region are obtained with a complexity of $O(n \log (n))$.
