Device-Independent quantum key distribution based on non-signaling constraints

Most of the existing quantum key distribution protocols do not consider the fact that the source and measuring device cannot be trusted, which causes hidden danger, such as the side channel attack, resulting in unsafe quantum communication. Therefore, it is important to research quantum key distribution protocol under the conditions of non-trusted device. We show a quantum key distribution protocol from correlation that violates a Bell inequality under the condition that both the source and the measurement devices are untrusted. We analyze its security under minimal assumptions (the non-signaling principle). We take noises and detection efficiency of the user's (Alice and Bob) detectors into account when bounding the secret key rate. We achieve a lower detection efficiency threshold, to compare with Ref. [Phys. Rev. A 85, 010301, (2012)], which means in the case of low efficiency of the detector, the key distribution can also be successfully completed.