  The guesswork is an information-theoretic quantity which can be seen as an
alternate security criterion to entropy. Recent work has established the
theoretical framework for guesswork in the presence of quantum side
information, which we extend both theoretically and experimentally. We consider
guesswork when the side information consists of the BB84 states and their
higher-dimensional generalizations. With this side information, we compute the
guesswork for two different scenarios for each dimension. We then perform a
proof-of-principle experiment using Laguerre-Gauss modes to experimentally
compute the guesswork for higher-dimensional generalizations of the BB84
states. We find that our experimental results agree closely with our
theoretical predictions. This work shows that guesswork can be a viable
security criterion in cryptographic tasks, and is experimentally accessible
across a number of optical setups.
