Gaussian-modulated coherent-state measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD), leaving the detection procedure to the third partner and thus being immune to all detector side-channel attacks, is very promising for the construction of high-security quantum information networks. We propose a scheme to implement MDI-QKD, but with continuous variables instead of discrete ones, i.e., with the source of Gaussian-modulated coherent states, based on the principle of continuous-variable entanglement swapping. This protocol not only can be implemented with current telecom components but also has high key rates compared to its discrete counterpart; thus it will be highly compatible with quantum networks.

Figure 1

Schematic setup of the continuous-variable MDI-QKD protocol. BHD: balanced homodyne detector; BS: balanced beam splitter.

Figure 2

Entangling cloner attack corresponding to two Markovian memoryless Gaussian channels with no interactions. Eve interacts Alice's and Bob's modes with her half of each EPR pair, respectively, and stores her ancillary modes ${\widehat{E}}_1^{{}^{\prime }},{\widehat{E}}_1^{{}^{\prime \prime }},{\widehat{E}}_2^{{}^{\prime }},{\widehat{E}}_2^{{}^{\prime \prime }}$ in her quantum memory to acquire information by collective measurements at any time of the data-processing procedure. $N_1$ ($N_2$) denotes the variance of each mode of the first EPR pair (the second EPR pair). The mode ${\widehat{E}}_3\in \{\widehat{Q},\widehat{P}\}$ is the virtual mode disclosed to Eve by Charlie's BSM, and it can be taken as a classical variable.

Figure 3

Secret key rates vs transmission distances between Alice, Charlie, and Bob for DR with symmetric channels. From top to bottom, excess noise is selected as 0, 0.005, 0.01, and 0.015, which are typical values in experiments [35]. Alice and Bob's modulation variance is set to be optimal, and the reconciliation efficiency is 0.95, which is an appropriate value (see [26]). Here, fiber loss is 0.2 dB/km.

Figure 4

Secret key rates vs transmission distances between Alice, Charlie, and Bob for RR with symmetric channels. From top to bottom, excess noise is selected as 0, 0.005, 0.01, and 0.015. Alice and Bob's modulation variance is also set to be optimal. Fiber loss is 0.2 dB/km, and the reconciliation efficiency is 0.95.

Figure 5

Secret key rates vs transmission distances between Alice, Charlie, and Bob for (a) RR and (b) DR in the asymmetric channel case with the optimal modulation variance. Excess noises are selected as 0 (solid lines), 0.005 (dashed lines), and 0.01 (dotted lines) for both channels referred to their respective channel transmissions $T_1$ and $T_2$. Both BSM relays are close to Alice's station, and the distance is set to be 10 m. Fiber loss is 0.2 dB/km, and the reconciliation efficiency is 0.95.

Figure 6

Schematic setup for measuring phase difference between two classical LO beams. PD: photodetector; BS1, BS2: beam splitters; all beam splitters in the figure are balanced, or 50:50.

Figure 7

Asymptotic key rates vs transmission distances between Alice, Charlie, and Bob for RR in the symmetric channel case with infinitely large modulation variance and perfect reconciliation efficiency, i.e., $V\to \infty$ and $\beta =1$. From top to bottom, excess noise is selected as 0, 0.005, 0.01, and 0.015. Fiber loss is 0.2 dB/km.