Unconditional Security Proof of Long-Distance Continuous-Variable Quantum Key Distribution with Discrete Modulation

We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.

Figure 1

Left: correlation $Z_{\mathrm{EPR}}$ of an EPR pair (solid line) and correlation $Z$ of state $|\Phi ⟩$ (dashed line) as a function of the modulation variance. Right: practical reconciliation efficiency for a binary modulation (dashed line) and for a Gaussian modulation (solid line) [18].

Figure 2

Secret key rate as a function of the distance for different values of the excess noise: from top to bottom, $\xi =0.002$, 0.004, 0.006, 0.008, 0.01. The quantum efficiency of Bob’s detection is $\eta =0.6$.