Mitigating finite key effects in the BB84 protocol using spontaneous parametric sources

The transmission of a limited number of quantum states constrains the length of the generated secret key. A parametric down-conversion source addresses this limitation by producing photon pairs, where one photon, the idler, carries the encoded information, while the other, the signal, is used for local detection to improve the signal-to-noise ratio of the communication. The separation of transmitted states based on the idler photon detection modifies the emission statistics, creating an effect similar to an intensity modulation scheme. By applying the decoy theory for arbitrary statistics, the secret key rate per quantum state can be increased by up to 40% compared to the BB84 protocol implemented with a 1-decoy intensity, in case of limited block sizes.