Security of quantum key distribution with light sources that are not independently and identically distributed

Although quantum key distribution (QKD) is theoretically secure, there is a gap between the theory and practice. In fact, real-life QKD may not be secure because component devices in QKD systems may deviate from the theoretical models assumed in security proofs. To solve this problem, it is necessary to construct the security proof under realistic assumptions on the source and measurement unit. In this paper, we prove the security of a QKD protocol under practical assumptions on the source that accommodate fluctuation of the phase and intensity modulations. As long as our assumptions hold, it does not matter at all how the phase and intensity distribute or whether or not their distributions over different pulses are independently and identically distributed. Our work shows that practical sources can be safely employed in QKD experiments.

Figure 1

Secret key generation rate (per pulse) vs fiber length for the first simulation. The phase fluctuates at most $\pm \theta$ except with the probability ${\delta }_{\theta }={10}^{-7}$. The key rates are plotted in logarithmic scale for $\theta =0,1,3,5,7,\text{and}{9}^{\circ }$ (from right to left).

Figure 2

Secret key generation rate (per pulse) vs fiber length for the second simulation. The phase (intensity) fluctuates at most $\pm \theta$ ($\pm x$%) except with the probability ${\delta }_{\theta }={10}^{-7}$ (${\delta }_{\mu }={10}^{-7}$). Numerically optimized secret key rates (in logarithmic scale) are obtained for $(\theta ,x)=(0^{\circ },0),(1^{\circ },1),(3^{\circ },3),(5^{\circ },5),(7^{\circ },7)$ (from right to left).

Figure 3

Top (bottom): The optimal value of ${\overline{\mu }}_{\mathrm{s}}$ (${\overline{\mu }}_{\mathrm{d}1}$) given the fiber length for the second simulation. The optimal values are plotted for $(\theta ,x)=(0^{\circ },0),(1^{\circ },1),(3^{\circ },3),(5^{\circ },5),(7^{\circ },7)$ from right to left. Here, the plot colors in the top and bottom figures correspond to each other.