  Heisenberg's uncertainty principle implies that if one party (Alice) prepares
a system and randomly measures one of two incompatible observables, then
another party (Bob) cannot perfectly predict the measurement outcomes. This
implication assumes that Bob does not possess an additional system that is
entangled to the measured one; indeed the seminal paper of Einstein, Podolsky
and Rosen (EPR) showed that maximal entanglement allows Bob to perfectly win
this guessing game. Although not in contradiction, the observations made by EPR
and Heisenberg illustrate two extreme cases of the interplay between
entanglement and uncertainty. On the one hand, no entanglement means that Bob's
predictions must display some uncertainty. Yet on the other hand, maximal
entanglement means that there is no more uncertainty at all. Here we follow an
operational approach and give an exact relation - an equality - between the
amount of uncertainty as measured by the guessing probability, and the amount
of entanglement as measured by the recoverable entanglement fidelity. From this
equality we deduce a simple criterion for witnessing bipartite entanglement and
a novel entanglement monogamy equality.
