  Bell's theorem, stating that quantum predictions are incompatible with a
local hidden variable description, is a cornerstone of quantum theory and at
the center of many quantum information processing protocols. Over the years,
different perspectives on non-locality have been put forward as well as
different ways to to detect non-locality and quantify it. Unfortunately and in
spite of its relevance, as the complexity of the Bell scenario increases,
deciding whether a given observed correlation is non-local becomes
computationally intractable. Here, we propose to analyse a Bell scenario as a
tensor network, a perspective permitting to test and quantify non-locality
resorting to very efficient algorithms originating from compressed sensing and
that offer a significant speedup in comparison with standard linear programming
methods. Furthermore, it allows to prove that non-signalling correlations can
be described by hidden variable models governed by a quasi-probability.
