  Device-independent quantum key distribution (DIQKD) is
information-theoretically secure against adversaries who possess a scalable
quantum computer and who have supplied malicious key-establishment systems;
however, the DIQKD key rate is currently too low. Consequently, we devise a
DIQKD scheme based on the quantum nonlocal Mermin-Peres magic square game: our
scheme asymptotically delivers DIQKD against collective attacks, even with
noise. Our scheme outperforms DIQKD using the Clauser-Horne-Shimony-Holt game
with respect to the number of game rounds, albeit not number of entangled
pairs, provided that both state visibility and detection efficiency are high
enough.
