Quantum key distribution without reference frame alignment: Exploiting photon orbital angular momentum

We present a new implementation of the BB84 quantum key distribution protocol that employs a $d$-dimensional Hilbert space spanned by spatial modes of the propagating beam that have a definite value of orbital angular momentum. Each photon carries $\log d$ bits of information, increasing the key generation rate of the protocol. The states used in the transmission part of the protocol are invariant under rotations about the propagation direction, making this implementation independent of the alignment between the reference frames of the sender and receiver. The protocol still works when these reference frames rotate with respect to each other.