  The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our
understanding of quantum mechanics, and is associated with the possibility of
predicting the results of non-commuting measurements with a precision that
seems to violate the uncertainty principle. This apparent contradiction to
complementarity is made possible by nonclassical correlations stronger than
entanglement, called steering. Quantum information recognises steering as an
essential resource for a number of tasks but, contrary to entanglement, its
role for metrology has so far remained unclear. Here, we formulate the EPR
paradox in the framework of quantum metrology, showing that it enables the
precise estimation of a local phase shift and of its generating observable.
Employing a stricter formulation of quantum complementarity, we derive a
criterion based on the quantum Fisher information that detects steering in a
larger class of states than well-known uncertainty-based criteria. Our result
identifies useful steering for quantum-enhanced precision measurements and
allows one to uncover steering of non-Gaussian states in state-of-the-art
experiments.
