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

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