We construct a new secret-key assisted polar coding scheme for private
classical communication over a quantum or classical wiretap channel. The
security of our scheme rests on an entropic uncertainty relation, in addition
to the channel polarization effect. Our scheme achieves the symmetric private
information rate by synthesizing "amplitude" and "phase" channels from an
arbitrary quantum wiretap channel. We find that the secret-key consumption rate
of the scheme vanishes for an arbitrary degradable quantum wiretap channel.
Furthermore, we provide an additional sufficient condition for when the secret
key rate vanishes, and we suspect that satisfying this condition implies that
the scheme requires no secret key at all. Thus, this latter condition addresses
an open question from the Mahdavifar-Vardy scheme for polar coding over a
classical wiretap channel.Comment: 11 pages, 2 figures, submission to the 2012 International Symposium
on Information Theory and its Applications (ISITA 2012), Honolulu, Hawaii,
US