Device-independent parallel self-testing of two singlets

Device-independent self-testing offers the possibility of certifying the quantum state and measurements, up to local isometries, using only the statistics observed by querying uncharacterized local devices. In this paper we study parallel self-testing of two maximally entangled pairs of qubits; in particular, the local tensor product structure is not assumed but derived. We prove two criteria that achieve the desired result: a double use of the Clauser-Horne-Shimony-Holt inequality and the 33 magic square game. This demonstrate that the magic square game can only be perfectly won by measuring a two-singlet state. The tolerance to noise is well within reach of state-of-the-art experiments.