Discrete-phase-randomized measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution removes all detector-side attacks in quantum cryptography, and in the meantime doubles the secure distance. The source side, however, is still vulnerable to various attacks. In particular, the continuous phase randomization assumption on the source side is normally not fulfilled in experimental implementation and may potentially open a loophole. In this work, we first show that indeed there are loopholes for imperfect phase randomization in measurement-device-independent quantum key distribution by providing a concrete attack. Then we propose a discrete-phase-randomized measurement-device-independent quantum key distribution protocol as a solution to close this source-side loophole.

Figure 1

Diagram of the MDI-QKD protocol. There are three modules, including Alice, Bob, and Eve. Alice and Bob generate source states, whereas the measurement device controlled by Eve performs a joint measurement on the states of Alice and Bob. Here, WCP stands for a weak coherent source; PM stands for a phase modulator; Decoy-IM stands for an intensity modulator that switches between the signal states and the decoy states. Conv is a converter that converts the phase encoding to the polarization encoding [9]; BS is a beam splitter; PBS is a polarization beam splitter; $D_{1H}$, $D_{1V}$, $D_{2H}$, $D_{2V}$ are single-photon detectors.

Figure 2

The relation between the key rate and the transmission distance for continuously random phases and discrete phases. The dashed line is the key rate for continuously random phases and the solid lines from left to right are for 9, 10, 11, 12, and 14 discrete phases, respectively.

Figure 3

The relation between the key rate and the noise level for continuously random phases and discrete phases. The dashed line is the key rate for continuously random phases and the solid lines from left to right are for 9, 10, 11, 12, and 14 discrete phases, respectively.