On the quantum-mechanical bound on the loss of information through side channels in quantum cryptography

The security of cryptographic keys in quantum cryptography systems is guaranteed by fundamental quantum mechanical exclusion principles. A quantum channel through which quantum states are transferred is not controlled and an eavesdropper can perform any modifications with it. The security of quantum key distribution protocols has already been proved [M. Tomamichel et al., Nature Commun. 3, 634 (2011); S. N. Molotkov, J. Exp. Theor. Phys. 115, 969 (2012)], including the realistic case of a finite length of transmitted sequences. It is always assumed that the eavesdropper has neither direct nor indirect access to the transmitting and receiving equipment. The real situation is somewhat different. The preparation and detection of quantum states occur according to random sequences that are generated on the transmitter and receiver sides. Detecting electromagnetic radiation generated in these processes, the eavesdropper can obtain additional information on a key. The upper quantum-mechanical bound on the amount of information of the eavesdropper on the key that can be obtained through a side channel has been determined.