Self-testing of Pauli observables for device-independent entanglement certification

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.