  We derive a new steering inequality based on a fine-grained uncertainty
relation to capture EPR-steering for bipartite systems. Our steering inequality
improves over previously known ones since it can experimentally detect all
steerable two-qubit Werner state with only two measurement settings on each
side. According to our inequality, pure entangle states are maximally
steerable. Moreover, by slightly changing the setting, we can express the
amount of violation of our inequality as a function of their violation of the
CHSH inequality. Finally, we prove that the amount of violation of our steering
inequality is, up to a constant factor, a lower bound on the key rate of a
one-sided device independent quantum key distribution protocol secure against
individual attacks. To show this result, we first derive a monogamy relation
for our steering inequality.
