  What is the minimum number of guesses needed on average to correctly guess a
realization of a random variable? The answer to this question led to the
introduction of the notion of a quantity called guesswork by Massey in 1994,
which can be viewed as an alternate security criterion to entropy. In this
paper, we consider the guesswork in the presence of quantum side information,
and show that a general sequential guessing strategy is equivalent to
performing a single measurement and choosing a guessing strategy from the
outcome. We use this result to deduce entropic one-shot and asymptotic bounds
on the guesswork in the presence of quantum side information, and to formulate
a semi-definite program (SDP) to calculate the quantity. We evaluate the
guesswork for a simple example involving the BB84 states, both numerically and
analytically, and prove a continuity result that certifies the security of
slightly imperfect key states when the guesswork is used as the security
criterion.
