Sufficiency of quantum non-Gaussianity for discrete-variable quantum key distribution over noisy channel

Quantum key distribution can be enhanced and extended if nonclassical single-photon states of light are used. We study a connection between the security of quantum key distribution and quantum non-Gaussianity of light arriving at the receiver's detection system after the propagation through a noisy quantum channel, being under full control of an eavesdropper performing general collective attacks. We show that while quantum nonclassicality exhibited by the light arriving at the receiver's station is a necessary indication of the security of the discrete-variable protocols, quantum non-Gaussianity can be a sufficient indication of their security. Therefore, checking for non-Gaussianity of this light by performing standard autocorrelation function measurement can be used for prior verification of the usability of prepare-and-measure schemes. It can play similar role to the prior verification of the quantum correlations sufficient to violate Bell inequalities for entanglement-based protocols.