Analysis of an injection-locking-loophole attack from an external source for quantum key distribution

Many security loopholes exist in quantum key distribution (QKD) due to the imperfections of realistic devices. On the source side, the decoy-state method can defend against the most severe photon-number-splitting (PNS) attack and improve the performance of QKD. Measurement-device-independent QKD and twin-field QKD have further closed all loopholes on the detection side. In this paper, we propose a valuable optical injection-locking loophole for the case when the internal isolator inside the laser is removed. We first introduce the effects of the injection locking with different injection intensities on the source frequency. Through the successive responses of adjacent pulses from frequency ports of the dense wavelength division multiplexer, the decoy state and the signal state can be partially distinguished. The specific injection-locking-loophole analysis of the isolatorless decoy phase-encoding Bennet-Brassard 1984 QKD and decoy phase-matching QKD protocols with external optical injection has been deeply studied. Simulation results show that, if we maintain the same observed gain statistics as normal after an external optical injection locking, the loophole cannot be exploited for a PNS attack when the QKD distance is short. As the QKD distance increases, a PNS attack at a medium distance using the optical injection-locking loophole does not threaten the security; the security is still valid. With the further increase of the QKD distance, the lower-bound secure key rate is higher than the upper-bound secure key rate given by a PNS attack at a long distance, some of the keys must be insecure, and information will be leaked.

Figure 1

Experimental setup of the single-optical-injection semiconductor laser. IM: intensity modulator, CIR: circulator, BS: beam splitter, PD: photodetector, OSA: optical spectrum analyzer, OSC: oscilloscope.

Figure 2

The black and pink solid lines are the experimental spectra of the slave laser with injection intensities $I_1$ and $I_2$. The black and red dashed lines are the experimental spectra of the free-running master and slave lasers. The middle green, right black, and left red dotted lines represent the reference frequencies $f_0, f_1$, and $f_2$.

Figure 3

The optical injection-locking-loophole analysis scheme for isolatorless decoy phase-encoding BB84-QKD. IM: intensity modulator, PM: phase modulator, BS: beam splitter, DWDM: dense wavelength division multiplexer, SNSPD: superconducting-nanowire single-photon detector.

Figure 4

The optical injection-locking-loophole analysis scheme for isolatorless decoy PM-QKD. IM: intensity modulator, PM: phase modulator, BS: beam splitter, DWDM: dense wavelength division multiplexer, EDFA: erbium-doped optical fiber amplifier, PD: photodetector, SNSPD: superconducting-nanowire single-photon detector.

Figure 5

The secure key rate of the isolatorless decoy phase-encoding BB84-QKD. The red solid line is the lower bound without a PNS attack. The black dashed line is the upper bound under the optical injection-locking loophole with a PNS attack.

Figure 6

The secure key rate of the isolatorless decoy PM-QKD. The red solid line is the lower bound without a PNS attack. The black dashed line is the upper bound under the optical injection-locking loophole with a PNS attack.

Figure 7

Intensity time series of optical injection locking. (a) $k_{\text{M}}$ = 90 GHz and (b) $k_{\text{M}}$ = 40 GHz.