Performance improvement of continuous-variable quantum key distribution via photon subtraction

It has been found that non-Gaussian operations can be applied to increase and distill entanglement between Gaussian entangled states. We propose here a method to improve the performance of entanglement-based (EB) continuous-variable quantum-key-distribution protocol by using the non-Gaussian operation, in particular, the subtraction operation, which can be implemented under current technology easily. Security analysis shows that the subtraction operation can well increase the secure distance and tolerable excess noise of the EB scheme and also the corresponding prepare-and-measure scheme.

Figure 1

The Gaussian modulation EB CVQKD protocol with non-Gaussian operations. PNRD stands for photon number resolving detector.

Figure 2

Comparison of the logarithmic negativity for state ${|\Psi \rangle }_{AB}$ [dashed (red) curve] and $|{\Psi }^{\left(1\right)}{\rangle }_{A{B}_1}$ for the non-Gaussian operations [solid (blue) curve] as the function of $\alpha$ with $\mu =0.5$.

Figure 3

Asymptotic secret key rate ${\tilde{K}}_N$ of the EB scheme with photon subtraction (thin curves), and $K_G$ of the original scheme (thick curves) as a function of distance for different values of the excess noise: the solid (red), dashed (purple), dotted (blue), and dot-dashed (green) curves correspond to $\varepsilon =0.01,$ 0.02, 0.03, and 0.05, respectively.

Figure 4

Lower bound of tolerable channel excess noise for the EB scheme with photon subtraction [upper (red) curve], and the original scheme [lower (blue) curve] as a function of transmission efficiency.

Figure 5

Asymptotic secret key rate ${\tilde{K}}_N$ of the EB scheme with photon subtraction as a function of distance for high channel excess noise. From top to bottom, $\varepsilon =0.1,$ 0.12, 0.14, 0.15.

Figure 6

Asymptotic secret key rate ${\tilde{K}}_N$ as a function of $\mu$ for different values of the channel excess noise (solid curves) with given transmission efficiency $T=0.268$, and for different distance (dashed curves) with given channel excess noise $\varepsilon =0.01$. From top to bottom, $\varepsilon =0.01,$ 0.02, 0.03, and 0.05, and distance $d=20$, 50, 100, and 150 km.

Figure 7

Asymptotic secret key rate ${\tilde{K}}_N$ of the EB scheme with photon subtraction (solid curves), and $K_G$ of the original scheme (dashed curves) as a function of modulation variance $V_A$ with $\mu =0.5$, $\varepsilon =0.01$. From bottom to top, $d=20$, 50, 100, and 150 km.