  Nonlocality, which is the key feature of quantum theory, has been linked with
the uncertainty principle by fine-grained uncertainty relations, by considering
combinations of outcomes for different measurements. However, this approach
assumes that information about the system to be fine-grained is local, and does
not present an explicitly computable bound. Here, we generalize above approach
to general quasi-fine-grained uncertainty relations (QFGURs) which applies in
the presence of quantum memory and provides conspicuously computable bounds to
quantitatively link the uncertainty to entanglement and Einstein-Podolsky-Rosen
(EPR) steering, respectively. Moreover, our QFGURs provide a framework to unify
three important forms of uncertainty relations, i.e., universal uncertainty
relations, uncertainty principle in the presence of quantum memory, and
fine-grained uncertainty relation. This result gives a direct significance to
the uncertainty principle, and allows us to determine whether a quantum
measurement exhibits typical quantum correlations, meanwhile, it reveals a
fundamental connection between basic elements of quantum theory, specifically,
uncertainty measures, combined outcomes for different measurements, quantum
memory, entanglement and EPR steering.
