Quantum key distribution with the single-photon-added coherent source

In this paper, we present schemes on implementing the single-photon-added coherent source in quantum key distributions. We apply this source in either the standard BB84 protocol or the recently proposed measurement-device-independent quantum key distribution, comparing their performance with the cases of using other existing sources, e.g., the weak coherent source or the heralded single-photon source, and giving out corresponding numerical simulations. Our simulation results show that in both protocols the single-photon-added coherent source can greatly exceed all other existing sources. Moreover, even when taking statistical fluctuation into account, a high key generation rate can still be achieved at long distance by applying this source.

Figure 1

Three-dimensional plot of the key generation rate changing with the intensity of either signal states $\left({\mu }^{\prime }\right)$ or decoy states $\left(\mu \right)$ in the standard BB84 protocol. Here we fix the transmission distance at 50 km.

Figure 2

Key generation rates vs transmission distance for the standard decoy-state QKD using SPACSs with different intensities. The curve $S_0$ represents the result of using infinite number of decoy states, and $S_1$ and $S_2$ are the results of using two-intensity decoy-state methods. Here, we set ${\mu }^{\prime }=1.10$ for all three curves, and $\mu =1.02$ or $1.04$ for $S_1$ and $S_2$ respectively.

Figure 3

Comparison of the key generation rates by using different sources (SPACS, WCS, HSPS, and SPS) in the standard BB84 protocol. Here we set ${\mu }^{\prime }=1.10,\mu =1.02$ for SPACS. For both WCS and HSPS, we set $\mu =0.1$, and use optimal values of ${\mu }^{\prime }$ at each distance. $S_0$ and $S_1$ represent the results of using infinite decoy-state method and two-intensity decoy-state method with SPACS, respectively. Each of $W_0$ and $W_1$($H_0$ and $H_1$) refers to using infinite decoy-state method or three-intensity decoy-state method with WCS (HSPS), individually. The grey solid curve is the result of ideal SPS.

Figure 4

A schematic setup of MDI-QKD using the SPACSs. Alice and Bob randomly prepare SPACSs in a BB84 polarization state with a polarization rotator (PR). Signal pulses from Alice and Bob interfere at a 50:50 beam splitter (BS) and then each enters a polarizing beam splitter (PBS) projecting the input photons into either horizontal (H) or vertical (V) polarization states. Four single-photon detectors are employed at the third party, Charlie's side, to detect the results.

Figure 5

Key generation rates for the MDI-QKD by using SPACS with different decoy states. $S_0$: with infinite decoy states; $S_1$ and $S_2$: with two-intensity decoy-state methods. For all curves we set ${\mu }^{\prime }=1.10$, and $\mu =1.02$ or $1.04$ for $S_1$ or $S_2$, individually.

Figure 6

Comparison of the key generation rates of the MDI-QKD by using SPACS, WCS, HSPS, and SPS. We set ${\mu }^{\prime }=1.10,\mu =1.02$ for SPACS. For both WCS and HSPS, we set $\mu =0.1$ and optimize the value of ${\mu }^{\prime }$ at each distance. $S_0$ and $S_1$: using infinite decoy states and two-intensity decoy-state method for SPACS; $W_0$ and $W_1$ ($H_0$ and $H_1$): using infinite decoy states and three-intensity decoy-state method for WCS (HSPS). The top solid curve is the result of using the ideal SPS.

Figure 7

Key generation rates of MDI-QKD using SPACS with statistical fluctuation, compared with the finite data case of using WCS. The black (grey) solid curve SPACS (WCS) refers to the case without statistical fluctuation, and the dashed (dotted) curves SPACS-f (WCS-f) represent the case when taking statistical fluctuation into account.

Figure 8

Key generation rates of standard BB84 QKD using SPACS with statistical fluctuation, compared with the finite data case of using WCS. The black (grey) solid curve SPACS (WCS) refers to the case without statistical fluctuation, and the dashed (dotted) curves SPACS-f (WCS-f) represent the case when taking statistical fluctuation into account.