Secure device-independent quantum key distribution with causally independent measurement devices

Device-independent quantum key distribution (QKD) aims to provide key distribution schemes, the security of which is based on the laws of quantum physics, but which does not require any assumptions about the internal working of the devices used in the protocol. This strong form of security is possible only when using correlations that violate a Bell inequality. Here, we provide a general security proof for a large class of protocols in a model in which the raw key is generated by independent measurements. This independence condition may be justifiable in several implementations and is necessarily satisfied when the raw key is generated by N separate pairs of devices. Our work shows that device-independent QKD is possible with key rates comparable to those of standard schemes.