State-discrimination attack on discretely modulated continuous-variable quantum key distribution

The continuous-variable quantum key distribution (CVQKD) schemes with discrete modulation are proposed to allow distributions of secret keys over long distance due to the sharing of discrete data. However, the nonorthogonal signal states in these schemes can be discriminated by using quantum receivers with low error rates, which may incur state-discrimination (SD) attacks. We consider the feasibility of Eve's attacks on discrete-modulated CVQKD protocol based on the SD receiver. In particular, an intercept-resend attack is proposed on the four-state protocol based on an SD receiver and a heralded noiseless linear amplifier. The security analysis shows that the secret key rate inferred by Alice and Bob can be larger than its true value, which reveals that the original four-state protocol is not secure under the SD attack. Fortunately, the decoy states can be well applied to remedy this defect, but with the cost of complicated practical implementation.

Figure 1

The intercept-resend attack for a four-state protocol based on the SD receiver.

Figure 2

The mutual information ${\chi }_{\text{BE}}$, $I_{\text{BE}}$, and $I_{\text{AB}}$ as a function of modulation variance $V_{\text{A}}$ of the four-state protocol under the SD attack for $g=1$, when the error probability of Eve's SD receiver $P_{\text{e}}$ values are (a) $P_{\text{SRM}}^g$ and (b) $P_{\text{SQL}}^g$, respectively.

Figure 3

The mutual information ${\chi }_{\text{BE}}$, $I_{\text{BE}}$, and $I_{\text{AB}}$ as a function of modulation variance $V_{\text{A}}$ of the four-state protocol under the SD attack for (a) $g=2$ when $P_{\text{e}}$ values $P_{\text{SRM}}^g$ and (b) $g=4$ when $P_{\text{e}}$ values $P_{\text{SQL}}^g$, respectively.

Figure 4

The mutual information ${\chi }_{\text{BE}}$, $I_{\text{BE}}$, and $I_{\text{AB}}$ as a function of modulation variance $V_{\text{A}}$ of the four-state protocol under the SD attack for (a) $g=4$ when $P_{\text{e}}$ values $P_{\text{SRM}}^g$ and (b) $g=6$ when $P_{\text{e}}$ values $P_{\text{SQL}}^g$, respectively.