Secure gated detection scheme for quantum cryptography

Several attacks have been proposed on quantum key distribution systems with gated single-photon detectors. The attacks involve triggering the detectors outside the center of the detector gate, and/or using bright illumination to exploit classical photodiode mode of the detectors. Hence a secure detection scheme requires two features: The detection events must take place in the middle of the gate, and the detector must be single-photon sensitive. Here we present a technique called bit-mapped gating, which is an elegant way to force the detections in the middle of the detector gate by coupling detection time and quantum bit error rate. We also discuss how to guarantee single-photon sensitivity by directly measuring detector parameters. Bit-mapped gating also provides a simple way to measure the detector blinding parameter in security proofs for quantum key distribution systems with detector efficiency mismatch, which up until now has remained a theoretical, unmeasurable quantity. Thus if single-photon sensitivity can be guaranteed within the gates, a detection scheme with bit-mapped gating satisfies the assumptions of the current security proofs.

Figure 1

Bit-mapped gating. (a) Detector gates with DEM. ${\eta }_a(t)$ (blue, dashed) and ${\eta }_b(t)$ (red, solid) are the efficiencies of the two detectors $a$ and $b$ with respect to time $t$. (b),(c) Possible optical bit mapping (teal) when the software bit mapping is set to $a\to 0$, $b\to 1$ (b) and $a\to 1$, $b\to 0$ (c). In a phase-encoded system the two levels would correspond to $0$ and $\pi$ phase shift in one basis, and $\pi /2$ and $3\pi /2$ phase shift in the opposite basis. Note that software bit mapping and optical bit mapping coincide in the bit-mapped gate, which is well within the detector gates. (d) ${\text{QBER}}_{min}(t)$ (green) as obtained from (8) with the bit-mapped gate shown in (b) and (c).

Figure 2

Curves (a) and (d) from Fig. 1. The dashed line shows how a threshold $E^{\prime }$ can be used to limit the range of modes $t$ used to calculate or bound ${\eta }^{\prime }$.

Figure 3

A calibrated light source inside Bob. The figure shows the Bob module in a plug-and-play system [4, 47, 48, 49], which has two possible implementations of the calibrated light source: either a separate attenuated laser diode (LD) at a suitable place, or in the case of send-return systems where Bob already contains a laser diode, a weakly reflective element (R) to reflect some light back into the APDs. In one-way systems [3, 50], Bob does not normally contain any light source, therefore a separate laser diode would be the only option. A short delay line (DL, $\text{delay}>\text{gate period}/2$) at Bob’s input guarantees that Eve cannot interfere with the detector operation based on whether the source is activated or not. PBS: polarizing beam splitter; Att.: optical attenuator; PM: phase modulator; $50:50$ fiber-optic coupler.