  As quantum technologies develop, we acquire control of an ever-growing number
of quantum systems. Unfortunately, current tools to detect relevant quantum
properties of quantum states, such as entanglement and Bell nonlocality, suffer
from severe scalability issues and can only be computed for systems of a very
modest size, of around $6$ sites. In order to address large many-body systems,
we propose a renormalisation-type approach based on a class of local linear
transformations, called connectors, which can be used to coarse-grain the
system in a way that preserves the property under investigation. Repeated
coarse-graining produces a system of manageable size, whose properties can then
be explored by means of usual techniques for small systems. In case of a
successful detection of the desired property, the method outputs a linear
witness which admits an exact tensor network representation, composed of
connectors. We demonstrate the power of our method by certifying using a normal
desktop computer entanglement, Bell nonlocality and supra-quantum Bell
nonlocality in systems with hundreds of sites.
