  This work considers the distribution of a secret key over an optical
(bosonic) channel in the regime of high photon efficiency, i.e., when the
number of secret key bits generated per detected photon is high. While in
principle the photon efficiency is unbounded, there is an inherent tradeoff
between this efficiency and the key generation rate (with respect to the
channel bandwidth). We derive asymptotic expressions for the optimal generation
rates in the photon-efficient limit, and propose schemes that approach these
limits up to certain approximations. The schemes are practical, in the sense
that they use coherent or temporally-entangled optical states and direct
photodetection, all of which are reasonably easy to realize in practice, in
conjunction with off-the-shelf classical codes.
