Experimental 4-intensity decoy-state quantum key distribution with asymmetric basis-detector efficiency

The decoy-state method has been developed rapidly in quantum key distribution (QKD) since it is immune to photon-number splitting attacks. We examine two-basis-detector-efficiency asymmetry, which exists in realistic scenarios. By using the recent 4-intensity decoy-state optimization protocol, we report an implementation of high-rate QKD with asymmetric basis-detector efficiency, demonstrating a 1.9 to 33.2 times higher key rate than previous protocols in the situation of large basis-detector-efficiency asymmetry. The results ruled out an implicit assumption in QKD that the efficiency of $Z$ basis and $X$ basis are restricted to be the same. This work paves the way towards a morepractical QKD setting.

Figure 1

Schematic layout of the experiment. DFB laser: distributed feedback laser; Att: manual attenuator; BS: beam splitter; PBS: polarization beam splitter; EVOA: electrical variable optical attenuator; CIR: circulator; FBG: fiber Bragg grating; DWDM: dense wavelength division multiplexer; SOA: semiconductor optical amplifier; EPC: electric polarization controller; PD: photoelectric detector; SPD: single-photon detector.

Figure 2

Experimental (symbols) and simulated (solid lines) secret key rates in bps versus the transmission distance from Alice to Bob $L$ in standard optical fiber. (a) The detector efficiency {${\eta }_Z,{\eta }_X$} is fixed at {10%, 5%}, while the experimental transmission distances are selected at 87, 126, 141, and 150 km. (b) The detector efficiency {${\eta }_Z,{\eta }_X$} is fixed at {10%, 1%}, while the experimental transmission distances are selected at 62, 87, 107, and 126 km. Blue squares, green diamonds, and red circles, respectively, refer to (I) traditional 3-intensity protocol [7] basis-detector efficiencies symmetry, where Bob reduces higher detecotor effiency to balance asymmetry ${\eta }_Z={\eta }_X=5\%\text{or}1\%$; (II) 3-intensity protocol with basis-detector efficiencies asymmetry [21], where $u_{X_2}=u_{Z_2},u_{X_1}=u_{Z_1},q_z=q_x,{\eta }_Z\ne {\eta }_X$; (III) 4-intensity protocol [21], where $u_{X_2}\ne u_{Z_2},u_{X_1}\ne u_{Z_1},q_Z\ne q_X,{\eta }_Z\ne {\eta }_X$. The experimental results are the average and variance (one standard deviation, assuming Poissonian detection statistics) of the final key rate calculated by 30 experiments. The advantage of the 4-intensity protocol is clearly verified by the experimental results, especially in a large degree of basis-detector efficiencies asymmetry. The results also confirm the excellent stability of three protocols used here.