Fundamental limits on key rates in device-independent quantum key distribution

In this paper, we introduce intrinsic non-locality as a quantifier for Bell non-locality, and we prove that it satisfies certain desirable properties such as faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation $p$. We also prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of any semi-device-independent protocol conducted using a device characterized by an assemblage $hat{rho}$. We also establish the faithfulness of intrinsic steerability and intrinsic non-locality. Finally, we prove that intrinsic non-locality is bounded from above by intrinsic steerability.