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 is an element of 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 [Bowles et al., Phys. Rev. Lea. 121, 180503 (2018)] and provides all the required technical proofs.