  Quantum theory allows for different classes of correlations, such as
entanglement, steerability or Bell-nonlocality. Experimental demonstrations of
the preparation of quantum states within specific classes and their subsequent
interconversion have been carried out; however, rigorous statements on the
statistical significance are not available. Behind this are two difficulties:
the lack of a method to derive a suitable confidence region from the measured
data and an efficient technique to classify the quantum correlations for every
state in the confidence region. In this work, we show how both of these
problems can be addressed. Specifically, we introduce a confidence polytope in
the form of a hyperoctahedron and provide a computationally efficient method to
verify whether a quantum state admits a local hidden state model, thus being
unsteerable and, consequently, Bell-local. We illustrate how our methods can be
used to analyse the activation of quantum correlations by local filtering,
specifically for Bell-nonlocality and quantum steerability.
