Fig. 3: The relation between Hmin(A∣E) and \(\hat{{p}_{\alpha }}\) with no afterpulse (Np), previous infinite afterpulse (Ip) and previous finite afterpulse (Fp), which consists of 1000 pulses.

The factors ωα = 0.001 and Aα are related to \(\hat{{p}_{\alpha }}\). The pulses with coherent states that contain ν = 10 photons insert SPDs with ηα = 0.1 and ed = 6 × 10−7. The shadow gap is the side information leaked to Eve due to the afterpulse.