Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator

We propose a pilot-multiplexed continuous-variable quantum key distribution (CVQKD) scheme based on a local local oscillator (LLO). Our scheme utilizes time-multiplexing and polarization-multiplexing techniques to dramatically isolate the quantum signal from the pilot, employs two heterodyne detectors to separately detect the signal and the pilot, and adopts a phase compensation method to almost eliminate the multifrequency phase jitter. In order to analyze the performance of our scheme, a general LLO noise model is constructed. Besides the phase noise and the modulation noise, the photon-leakage noise from the reference path and the quantization noise due to the analog-to-digital converter (ADC) are also considered, which are first analyzed in the LLO regime. Under such general noise model, our scheme has a higher key rate and longer secure distance compared with the preexisting LLO schemes. Moreover, we also conduct an experiment to verify our pilot-multiplexed scheme. Results show that it maintains a low level of the phase noise and is expected to obtain a 554-Kbps secure key rate within a 15-km distance under the finite-size effect.

Figure 1

The conventional LLO-CVQKD schematic. Alice first generates the signal and the pilot, both of which are then transmitted to Bob. On the other side, Bob produces the local LO to interfere with the signal and the pilot. After the heterodyne detection, Bob obtains the raw data as well as the phase drift information, which is then utilized to execute the phase compensation yielding the corrected data.

Figure 2

The procedure of the pilot-sequential scheme.

Figure 3

The procedure of the pilot-delayline scheme.

Figure 4

The procedure of the pilot-multiplexed scheme.

Figure 5

(a) The solid curve represents the key rate under the pilot-multiplexed scheme, while the dashed curves represent the key rate under the pilot-sequential scheme with the variable parameter $V_{\mathrm{drift}}=0.01,0.02,0.03$, respectively. And $d_{dB}$ is set as 80 dB for simplicity. (b) The solid curve represents the key rate under the pilot-multiplexed scheme, while the dash curves represent the key rate under the pilot sequential with the variable parameter $d_{dB}=30\mathrm{dB}$, 40 dB, and 50 dB, respectively. And $V_{\mathrm{drift}}$ is set as 0.01. (c) The solid curves represent the key rate under the pilot-multiplexed scheme with various extinction ratio $R_e=30\mathrm{dB}$, 40 dB, and 50 dB, while the dashed curves represent the key rate under the delayline scheme. And $n$ is set as 20 bit. (d) The solid curve represents the key rate under the pilot-multiplexed scheme with various quantization bit number $n=8,10,12$ bit, while the dash curves represent the key rate under the delayline scheme. And $R_e$ is set as 60 dB. In all the simulations, the amplitude of the pilot $|{\alpha }_R|$ is chosen to be optimal and the rest is excess noise due to other imperfections is set as 0.05. Other parameters are set as the modulation variance $V_A=4$, the quantum efficiency $\eta =0.6$, the electronic noise $v_{\mathrm{el}}=0.01$, the reconciliation efficiency $\beta =95\%$, and the typical polarization extinction ratio $R_{\mathrm{po}}=30\mathrm{dB}$. The key rate is calculated under the collective attacks with the heterodyne detection, and in the asymptotic limit for simplicity.

Figure 6

The configuration of pilot-multiplexed scheme. PBS, polarizing beam splitter; AM, amplitude modulator; PM, phase modulator; BS, beam splitter; PC, polarization controller; VOA, variable optical attenuator.

Figure 7

The procedure of the phase compensation. (a) The measured phase after detection. (b) The remapped signal phase after the fast-drift compensation. (c) The remapped signal phase after the slow-drift compensation. The red circle represents the measured signal phase, the blue star represents the measured pilot phase, and the blue dot represents the initial modulation phase.

Figure 8

Statistics histograms of the residual phase noise. In each histogram, 25 000 deviation values of the phase are counted and the variance of them is labeled above. From top to bottom, the photon numbers of the pilot pulse at the input of the balanced detector are $10000,1000,100$, respectively, while each case is repeated three times. The repetition rate in our experiment is 50 MHz and the signal is sampled by a broadband oscilloscope at a 2.5-GHz sampling rate.

Figure 9

Measured excess noise in shot noise units. The blue circles represent the measured noise with the block size of $5\times {10}^7$, while the red squares represent the worst excess noise considering the finite-size effect. The red and blue lines represent the mean of measured excess noise with the finite-size effect or not, respectively. The transmission distance is 15 km,the quantum efficiency is 0.4, and the electronic noise is 1.17.

Figure 10

Secret key rate in the pilot-multiplexed scheme under the finite-size effect. The red square represents the achievable secret key rate of 554 Kbps within a 15-km standard optical fiber. Parameters are typically set as the quantum efficiency $\eta =0.4$, the electronic noise $v_{\mathrm{el}}=1.17$, the achievable reconciliation efficiency $\beta =95\%$, the security parameters ${\epsilon }_{\mathrm{PE}}={\epsilon }_{\mathrm{PA}}=\overline{\epsilon }={10}^{-10}$, the block size $N={10}^8$, and the data size for parameter estimation $m=5\times {10}^7$.