A quantum linearity test for robustly verifying entanglement

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 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.