Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs

Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by laws mechanics. However, a practical implementation is still pending due to requirement combinations visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates search for DI-QKD protocols can close gap between theoretical security. In this work, we present two whose relies on Bell inequalities more than inputs outputs. We show that, maximally entangled states perfect visibility, protocol based inequality three four outputs requires slightly lower