Exploring the role of Leggett-Garg inequality for quantum cryptography

In the cryptographic context, an earlier unexplored application of the temporal version of the Bell-type inequality is shown here in the device-independent (DI) scenario. This is done by using the Leggett-Garg inequality (LGI) to demonstrate the security against eavesdropping in a quantum key distribution (QKD) scheme. This typically involves a higher dimensional attack against which the standard BB84 protocol is insecure. For this purpose, we invoke an appropriate form of LGI. While the key generation is done by the usual Bennett-Brassard 1984 (BB84) method, the security check against device attacks is provided by testing for the violation of the particular form of LGI used here.