  We present self-testing protocols to certify the presence of tensor products
of Pauli measurements on maximally entangled states of local dimension $2^n$
for $n\in\mathbb{N}$. This provides self-tests of sets of informationally
complete measurements in arbitrarily high dimension. We then show that this can
be used for the device-independent certification of the entanglement of all
bipartite entangled states by exploiting a connection to measurement
device-independent entanglement witnesses and quantum networks. This work
extends a more compact parallel work on the same subject and provides all the
required technical proofs.
