  Historically, the element of uncertainty in quantum mechanics has been
expressed through mathematical identities called uncertainty relations, a great
many of which continue to be discovered. These relations use diverse measures
to quantify uncertainty (and joint uncertainty). In this paper we use
operational information-theoretic principles to identify the common essence of
all such measures, thereby defining measure-independent notions of uncertainty
and joint uncertainty. We find that most existing entropic uncertainty
relations use measures of joint uncertainty that yield themselves to a small
class of operational interpretations. Our notion relaxes this restriction,
revealing previously unexplored joint uncertainty measures. To illustrate the
utility of our formalism, we derive an uncertainty relation based on one such
new measure. We also use our formalism to gain insight into the conditions
under which measure-independent uncertainty relations can be found.
