  Gathering data through measurements is at the basis of every experimental
science. Ideally, measurements should be repeatable and, when extracting only
coarse-grained data, they should allow the experimenter to retrieve the finer
details at a later time. However, in practice most measurements appear to be
noisy. Here we postulate that, despite the imperfections observed in real life
experiments, there exists a fundamental level where all measurements are ideal.
Combined with the requirement that ideal measurements remain so when
coarse-grained or applied in parallel on spacelike separated systems, our
postulate places a powerful constraint on the amount of nonlocality and
contextuality that can be found in an arbitrary physical theory, bringing down
the violation of Bell and Kocher-Specker inequalities near to its quantum
value. In addition, it provides a new compelling motivation for the principles
of Local Orthogonality and Consistent Exclusivity, recently proposed for the
characterization of the quantum set of probability distributions.
