  Non-orthogonal quantum states pose a fundamental challenge in quantum
information processing, as they cannot be distinguished with absolute
certainty. Conventionally, the focus has been on minimizing error probability
in quantum state discrimination tasks. However, another criterion known as
quantum guesswork has emerged as a crucial measure in assessing the
distinguishability of non-orthogonal quantum states, when we are allowed to
query a sequence of states. In this paper, we generalize well known properties
in the classical setting that are relevant for the guessing problem.
Specifically, we establish the pre and post Data Processing Inequalities. We
also derive a more refined lower bound on quantum guesswork.
