We introduce a simple two-player test which certifies that the players apply
tensor products of Pauli σX​ and σZ​ observables on the tensor
product of n EPR pairs. The test has constant robustness: any strategy
achieving success probability within an additive ε of the optimal
must be poly(ε)-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.Comment: 36 pages. Improves upon and supersedes our earlier submission
arXiv:1512.0209