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 [Bowles et al., Phys. Rev. Lett. 121, 180503 (2018)] and provides all the required technical proofs.

• Received 27 March 2018
• Revised 26 September 2018

DOI:https://doi.org/10.1103/PhysRevA.98.042336