  Quantum mechanics predicts that measurements of incompatible observables
carry a minimum uncertainty which is independent of technical deficiencies of
the measurement apparatus or incomplete knowledge of the state of the system.
Nothing yet seems to prevent a single physical quantity, such as one spin
component, from being measured with arbitrary precision. Here we show that an
intrinsic quantum uncertainty on a single observable is ineludible in a number
of physical situations. When revealed on local observables of a bipartite
system, such uncertainty defines an entire class of bona fide measures of
nonclassical correlations. For the case of 2 x d systems, we find that a unique
measure is defined, which we evaluate in closed form. We then discuss the role
that these correlations, which are of the 'discord' type, can play in the
context of quantum metrology. We show in particular that the amount of discord
present in a bipartite mixed probe state guarantees a minimum precision, as
quantified by the quantum Fisher information, in the optimal phase estimation
protocol.
