Quantum key distribution with entangled photon sources

A parametric down-conversion (PDC) source can be used as either a triggered single-photon source or an entangled-photon source in quantum key distribution (QKD). The triggering PDC QKD has already been studied in the literature. On the other hand, a model and a post-processing protocol for the entanglement PDC QKD are still missing. We fill in this important gap by proposing such a model and a post-processing protocol for the entanglement PDC QKD. Although the PDC model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. Since an entangled PDC source is a basis-independent source, we apply Koashi and Preskill’s security analysis to the entanglement PDC QKD. We also investigate the entanglement PDC QKD with two-way classical communications. We find that the recurrence scheme increases the key rate and the Gottesman-Lo protocol helps tolerate higher channel losses. By simulating a recent $144\text{−}\mathrm{km}$ open-air PDC experiment, we compare three implementations: entanglement PDC QKD, triggering PDC QKD, and coherent-state QKD. The simulation result suggests that the entanglement PDC QKD can tolerate higher channel losses than the coherent-state QKD. The coherent-state QKD with decoy states is able to achieve highest key rate in the low- and medium-loss regions. By applying the Gottesman-Lo two-way post-processing protocol, the entanglement PDC QKD can tolerate up to $70\mathrm{dB}$ combined channel losses ($35\mathrm{dB}$ for each channel) provided that the PDC source is placed in between Alice and Bob. After considering statistical fluctuations, the PDC setup can tolerate up to $53\mathrm{dB}$ channel losses.

Figure 1

A schematic diagram for the entanglement PDC QKD. Alice and Bob connect to a entangled PDC source by optical links. They each receive one of two entangled modes coming out from the PDC source. Both Alice and Bob randomly choose the basis (by polarization controllers) to measure the arrived signals (by single-photon detectors). PC: polarization controller. PBS: polarized beam splitter. ${\mathrm{DA}}_0$, ${\mathrm{DA}}_1$, ${\mathrm{DB}}_0$, ${\mathrm{DB}}_1$: threshold detectors.

Figure 2

A schematic diagram for the entanglement PDC QKD. Alice measures one of the entangled modes coming out from the PDC source and sends Bob the other mode.

Figure 3

(Color online) Plot of the key generation rate in terms of the optical loss, comparing four cases: coherent-state $\mathrm{QKD}+\mathrm{aysmptotic}$ decoy, triggering $\mathrm{PDC}+\mathrm{asymptotic}$ decoy, and entanglement PDC QKD (source in the middle and source on Alice’s side). For the coherent state $\mathrm{QKD}+\mathrm{decoy}$, we use ${\eta }_A=1$. We numerically optimize $\mu$ $\left(2\lambda \right)$ for each curve.

Figure 4

(Color online) Plot of the key generation rate in terms of the optical loss. We apply the recurrence idea and up to 3 $B$ steps. $\mu$ is numerically optimized for each curve.

Figure 5

(Color online) Plot of the key generation rate in terms of the optical loss. We take a realistic $\mu =2\lambda =0.053$ and consider the fluctuation with a data size of $N=1.5\times {10}^{11}$ and a confident interval of $1-P_{ϵ}\ge 1-e^{-50}$.

Figure 6

Plot of the optimal $\mu$ in terms of $e_d$ for the entanglement PDC QKD. $f\left(e_d\right)=1.22$.