Cloning and optimal Gaussian individual attacks for a continuous-variable quantum key distribution using coherent states and reverse reconciliation

We investigate the security of continuous-variable quantum key distribution using coherent states and reverse reconciliation against Gaussian individual attacks based on an optimal Gaussian $1\to 2$ cloning machine. We provide an implementation of the optimal Gaussian individual attack. We also find a Bell-measurement attack which works without delayed choice of measurements and has better performance than the cloning attack.

Figure 1

Eve’s attack is based on the Gaussian cloning machine which is constructed by a linear amplifier (AMP) followed by a beam splitter (BS).

Figure 2

(Color online) The security condition is shown for the line transmission $\eta$ and quadrature excess noise $\delta$ in the high-modulation limit $(V_A\to \infty )$. The dash-dotted line is for the cloning attack, the dotted line is for the anticloning attack, the dashed line is for the Bell-measurement attack, and the solid line is for the optimal Gaussian individual attack. The dot-dash-dotted line is for the intercept-resend attack which gives a necessary condition of CV QKD using coherent states [14, 15].