Quantum key distribution with dual detectors

To improve the performance of a quantum-key-distribution (QKD) system, high speed, low dark count single photon detectors (or low-noise homodyne detectors) are required. However, in practice, a fast detector is usually noisy. Here, we propose a dual-detector method to improve the performance of a practical QKD system with realistic detectors: the legitimate receiver randomly uses either a fast (but noisy) detector or a quiet (but slow) detector to measure the incoming quantum signals. The measurement results from the quiet detector can be used to bound the eavesdropper’s information, while the measurement results from the fast detector are used to generate a secure key. We apply this idea to various QKD protocols. Simulation results demonstrate significant improvements of the secure key rate in the lower loss regime in both Bennett-Brassard 1984 (BB84) protocol with ideal single photon source and Gaussian-modulated coherent states protocol; while for decoy-state BB84 protocol with weak coherent source, the improvement is moderate. We also discuss various practical issues in implementing the dual-detector scheme.

Figure 1

(Color online) Simulation results for the BB84 protocol with a single photon source. Simulation parameters: $\alpha =0.21\mathrm{dB}∕\mathrm{km}$, $f\left(x\right)=1.22$; $G_{\text{Bob}}=0.16$ and $e_{\det }=0.018$ [20]; $r_1=1\mathrm{GHz}$, ${\eta }_D^{\left(1\right)}=0.059$ and $Y_0^{\left(1\right)}=1.3\times {10}^{-5}$ [19]; $r_2=2.5\mathrm{MHz}$, ${\eta }_D^{\left(2\right)}=0.5$ and $Y_0^{\left(2\right)}=3\times {10}^{-7}$ [14]. The key rate of the dual-detector system is higher than either of the two single SPD systems up to $\sim 124\mathrm{km}$. Note that at a longer distance, when the system with SPD2 alone yields a higher key rate, Bob can simply use SPD2 itself.

Figure 2

(Color online) Simulation results for BB84 protocol with single photon source. Simulation parameters: $r_1=10\mathrm{GHz}$, ${\eta }_D^{\left(1\right)}=0.0027$, $Y_0^{\left(1\right)}=3.2\times {10}^{-9}$, and $e_{\det }^{\left(1\right)}=0.097$ [22]. Other parameters are same as in Fig. 1. The key rate of the dual-detector system is significantly higher than either of the two single SPD systems up to $\sim 200\mathrm{km}$. Note that no secure key can be produced by SPD1 alone at any distance.

Figure 3

(Color online) Simulation results for the BB84 protocol with a single photon source. Simulation parameters: $r_1=10\mathrm{GHz}$, ${\eta }_D^{\left(1\right)}=0.0027$, $Y_0^{\left(1\right)}=3.2\times {10}^{-9}$, and $e_{\det }^{\left(1\right)}=0.097$ [22]; $r_2=100\mathrm{MHz}$, ${\eta }_D^{\left(2\right)}=0.0027$, $Y_0^{\left(2\right)}=3.2\times {10}^{-9}$, and $e_{\det }^{\left(2\right)}=0.018$. Other parameters are the same as in Fig. 1. The key rate of the dual-detector system is significantly higher than either of the two single SPD systems up to $\sim 190\mathrm{km}$. Note that no secure key can be produced by SPD1 alone at any distance.

Figure 4

(Color online) Simulation results for the decoy state BB84 protocol with weak coherent source. Simulation parameters: $\alpha =0.21\mathrm{dB}∕\mathrm{km}$, $f\left(x\right)=1.22$, $\mu =0.73$; $G_{\text{Bob}}=0.16$ and $e_{\det }=0.018$ [20]; $r_1=1\mathrm{GHz}$, ${\eta }_D^{\left(1\right)}=0.059$, and $Y_0^{\left(1\right)}=1.3\times {10}^{-5}$ [19]; $r_2=2.5\mathrm{MHz}$, ${\eta }_D^{\left(2\right)}=0.5$, and $Y_0^{\left(2\right)}=3\times {10}^{-7}$ [14]. The key rate of the dual-detector system is higher than either of the two single SPD systems up to $\sim 82\mathrm{km}$. Note that even without doing any privacy amplification (PA), the improvement in this case is moderate.

Figure 5

(Color online) Simulation results for GMCS QKD with the DR protocol. Simulation parameters: $\alpha =0.21\mathrm{dB}∕\mathrm{km}$, $V=40$, $\beta =1$; $G_{\det }=0.8$, ${\epsilon }_{\mathrm{pre}}=0.05$ [25]; $r_1=82\mathrm{MHz}$, ${\epsilon }_{\det 1}=0.43$ [27]; $r_2=1\mathrm{MHz}$, ${\epsilon }_{\det 2}=0.01$ [25]. With the dual-detectors method, we see a significant improvement of the key rate (more than one order of magnitude) at relatively short distance (up to $5\mathrm{km}$).

Figure 6

(Color online) Simulation results for GMCS QKD with the RR protocol. Simulation parameters: $\alpha =0.21\mathrm{dB}∕\mathrm{km}$, $V=40$, $\beta =1$; $G_{\det }=0.8$, ${\epsilon }_{\mathrm{pre}}=0.05$ [25]; $r_1=82\mathrm{MHz}$, ${\epsilon }_{\det 1}=0.43$ [27]; $r_2=1\mathrm{MHz}$, ${\epsilon }_{\det 2}=0.01$ [25]. With the dual-detector method, we see a significant improvement of the key rate (more than one order of magnitude) at relatively short distance (up to $17\mathrm{km}$). Note that in this case, no positive key rate can be achieved with detector 1 alone at any distance.

Figure 7

(Color online) Simulation results for GMCS QKD with the realistic RR protocol. Simulation parameters: $\alpha =0.21\mathrm{dB}∕\mathrm{km}$, $V=20$, $\beta =0.8$; $G_{\det }=0.8$, ${\epsilon }_{\mathrm{pre}}=0.05$ [25]; $r_1=82\mathrm{MHz}$, ${\epsilon }_{\det 1}=0.43$ [27]; $r_2=1\mathrm{MHz}$, ${\epsilon }_{\det 2}=0.01$ [25]. With the dual-detector method, we see a significant improvement of the key rate (more than one order of magnitude) at relatively short distance (up to $5\mathrm{km}$). Note that in this case, no positive key rate can be achieved with detector 1 alone at any distance.

Figure 8

(Color online) Simulation results with a lossy $\left(3\mathrm{dB}\right)$ optical switch. Simulation parameters: $r_1=10\mathrm{GHz}$, ${\eta }_D^{\left(1\right)}=0.0027$, $Y_0^{\left(1\right)}=3.2\times {10}^{-9}$, and $e_{\det }^{\left(1\right)}=0.097$ [22]. Other parameters are the same as in Fig. 1. The key rate of the dual-detector system is significantly higher than either of the two single SPD systems up to $\sim 180\mathrm{km}$. Note that no secure key can be produced by SPD1 alone at any distance.

Figure 9

(Color online) Simulation results with a lossy $\left(3\mathrm{dB}\right)$ optical switch. Simulation parameters: $r_1=10\mathrm{GHz}$, ${\eta }_D^{\left(1\right)}=0.0027$, $Y_0^{\left(1\right)}=3.2\times {10}^{-9}$, and $e_{\det }^{\left(1\right)}=0.097$ [22]; $r_2=100\mathrm{MHz}$, ${\eta }_D^{\left(2\right)}=0.0027$, $Y_0^{\left(2\right)}=3.2\times {10}^{-9}$, and $e_{\det }^{\left(2\right)}=0.018$. Other parameters are the same as in Fig. 1. The key rate of the dual-detector system is significantly higher than either of the two single SPD systems up to $\sim 175\mathrm{km}$. Note that no secure key can be produced by SPD1 alone at any distance.