  Uncertainty relations play a significant role in drawing a line between
classical physics and quantum physics. Since the introduction by Heisenberg,
these relations have been considerably explored. However, the effect of quantum
entanglement on uncertainty relations was not probed. Berta et al. [Nature
Physics 6, 659-662 (2010)] removed this gap by deriving a conditional-entropic
uncertainty relation in the presence of quantum entanglement. In the same
spirit, using inferred-variance, we formulate uncertainty relations in the
presence of entanglement for general two-qubit systems and arbitrary
observables. We derive lower bounds for the sum and product inferred-variance
uncertainty relations. Strikingly, we can write the lower bounds of these
inferred-variance uncertainty relations in terms of measures of entanglement of
two-qubit states, as characterized by concurrence, or $G$ function. Presumably,
the presence of entanglement in the lower bound of inferred-variance
uncertainty relation is new and unique. We also explore the violation of local
uncertainty relations in this context and an interference experiment.
Furthermore, we discuss possible applications of these uncertainty relations.
