Quantum key distribution with any two independent and identically distributed states

To prove the security of quantum key distribution (QKD) protocols, several assumptions have to be imposed on users’ devices. From an experimental point of view, it is preferable that such theoretical requirements are feasible and the number of them is small. In this paper, we provide a security proof of a QKD protocol where the usage of any light source is allowed as long as it emits two independent and identically distributed (i.i.d.) states. Our QKD protocol is composed of two parts: the first part is characterization of the photon-number statistics of the emitted signals up to three-photons based on the method [Opt. Exp. 27, 5297 (2019)], followed by running our differential-phase-shift (DPS) protocol [npj Quantum Inf. 5, 87 (2019)]. It is remarkable that as long as the light source emits two i.i.d. states, even if we have no prior knowledge of the light source, we can securely employ it in the QKD protocol. As this result substantially simplifies the requirements on light sources, it constitutes a significant contribution on realizing truly secure quantum communication.