Practical security of continuous-variable quantum key distribution with finite sampling bandwidth effects

Practical security of the continuous-variable quantum key distribution (CVQKD) system with finite sampling bandwidth of analog-to-digital converter (ADC) at the receiver's side is investigated. We find that the finite sampling bandwidth effects may decrease the lower bound of secret key rate without awareness of the legitimate communicators. This leaves security loopholes for Eve to attack the system. In addition, this effect may restrains the linear relationship of secret key bit rate with repetition rate of the system; subsequently, there is a saturation value for the secret key bit rate with the repetition rate. To resist such kind of effects, we propose a dual sampling detection approach in which two ADCs are employed so that the finite sampling bandwidth effects are removed.

Figure 1

Realistic homodyne detection scheme in pulsed CVQKD system. A power meter is used to measure the intensity of LO in real time. Output signal of homodyne detector is sampled by an ADC with sampling frequency $f_{\mathrm{samp}}.$

Figure 2

Time-domain shape of an output pulse from the balanced homodyne detector with sampling interval of $t_S$. Red circles are the sampled points got by Bob. $U_p$ presents the peak value of the pulse and $U_m$ is the maximal measured value.

Figure 3

The estimated excess noise as a function of the system repetition rate under different channel excess noise. Sampling bandwidth $f_{\mathrm{samp}}$ is fixed to 1 GHz and channel transmittance is 0.1. Curves from top to bottom represent $\varepsilon =0.04, \varepsilon =0.02, \varepsilon =0.01$.

Figure 4

The security bound of CVQKD system with finite sampling bandwidth effects. Sampling bandwidth is fixed to 1 GHz and the measured excess noise is assumed to be 0.01. Modulation variance $V_A=5$. (a) The secret key rate $K$ as a function of the transmission distance. Curves from top to bottom represent the case without considering the bandwidth, $f_{\mathrm{rep}}=2\mathrm{MHz}, f_{\mathrm{rep}}=5\mathrm{MHz}$, and $f_{\mathrm{rep}}=8\mathrm{MHz}$, respectively. (b) The secret bit rate $R$ as a function of the system repetition rate. Curves from top to bottom represent the $L=20\mathrm{km}, L=40\mathrm{km}$ and $L=60\mathrm{km}$, respectively.

Figure 5

The countermeasure: dual sampling detection scheme. Both LO and homodyne output signal are measured by ADCs with $f_{\mathrm{samp}}$ sampling bandwidth.

Figure 6

The security bound of CVQKD system with the dual sampling detection scheme. (a) The secret key rate $K$ as a function of the transmission distance. Curves from top to bottom represent $f_{\mathrm{rep}}=100\mathrm{MHz}, f_{\mathrm{rep}}=80\mathrm{MHz}$, and $f_{\mathrm{rep}}=50\mathrm{MHz}$ and the case without considering the bandwidth. (b) The secret bit rate $R$ as a function of $f_{\mathrm{rep}}$. Curves from top to bottom represent $L=20\mathrm{km}, L=40\mathrm{km},$ and $L=60\mathrm{km}$, respectively.