  Quantum key distribution (QKD) offers the possibility for two individuals to
communicate a securely encrypted message. From the time of its inception in
1984 by Bennett and Brassard, QKD has been the result of intense research. One
technical challenge is the monitoring of signal disturbance in a QKD system to
bound the information leakage towards an unwanted eavesdropper. Recently, the
round-robin differential phase-shift (RRDPS) protocol, which encodes bits of
information in a high-dimensional state space, was proposed to solve this exact
problem. Since its introduction, many realizations of the RRDPS protocol were
demonstrated using trains of coherent pulses. Here, we propose and
experimentally demonstrate an implementation of the RRDPS protocol using the
photonic orbital angular momentum degree of freedom. In particular, we show
that Alice's generation stage and Bob's detection stage can each be reduced to
a single phase element, greatly simplifying its implementation. Our scheme
offers a practical demonstration of the RRDPS protocol which will suppress the
need for monitoring signal disturbance in free-space channels.
