  The coding space in quantum communication could be expanded to
high-dimensional space by using orbital angular momentum (OAM) states of
photons, as both the capacity of the channel and security are enhanced. Here we
present a novel approach to realize high-capacity quantum key distribution
(QKD) by exploiting OAM states. The innovation of the proposed approach relies
on a unique type of entangledphoton source which produces entangled photons
with OAM randomly distributed among high order Fiboncci-like numbers and a new
physical mechanism for efficiently sharing keys. This combination of
entanglement with mathematical properties of high order Fibonacci sequences
provides the QKD protocol which is immune to photon-number-splitting attacks
and allows secure generation of long keys from few photons. Unlike other
protocols, reference frame alignment and active modulation of production and
detection bases are unnecessary.
