  We introduce a simple two-player test which certifies that the players apply
tensor products of Pauli $\sigma_X$ and $\sigma_Z$ observables on the tensor
product of $n$ EPR pairs. The test has constant robustness: any strategy
achieving success probability within an additive $\varepsilon$ of the optimal
must be $\mathrm{poly}(\varepsilon)$-close, in the appropriate distance
measure, to the honest $n$-qubit strategy. The test involves $2n$-bit questions
and $2$-bit answers. The key technical ingredient is a quantum version of the
classical linearity test of Blum, Luby, and Rubinfeld.
  As applications of our result we give (i) the first robust self-test for $n$
EPR pairs; (ii) a quantum multiprover interactive proof system for the local
Hamiltonian problem with a constant number of provers and classical questions
and answers, and a constant completeness-soundness gap independent of system
size; (iii) a robust protocol for delegated quantum computation.
