Fig. 1. Silicon-based QKD system. (a) Schematic of the QKD setup. Laser, laser diode; Encoder, silicon chip integrating an intensity modulator and a polarization state modulator; VOA, variable optical attenuator; Decoder, polarization state demodulation chip; SNSPD, superconducting nanowire single photon detector; TDC, time digital converter; AWG, arbitrary waveform generator; DC, programmable DC power supply; Delayer, home-made time delay generator. (b) Schematic of the encoder. MMI, multimode interferometer; PS, thermo-phase shifter; CDM, carrier-depletion modulator; 1-D, one-dimensional grating coupler; 2-D, two-dimensional grating coupler; IM, intensity modulator; Pol-M, polarization modulator. (c) Schematic of the decoder. SSC, spot-size converter; PSR, polarization splitter-rotator. (d) Picture of the packaged encoder chip soldered to the external control board. (e) Picture of the packaged decoder chip soldered to the external control board.

Fig. 2. QBER on Z  (X) basis of the system without active feedback over 6 h. The red (blue) points represent the quantum bit error in Z  (X) basis. Each point is refreshed every 1 s.

Fig. 3. QBER measurements for a 50 km fiber channel over 2.4 h operation. During the measurement process, an increased voltage at a step of 1 V is applied to the fiber scrambler every 5 min to mimic the polarization drift of the fiber channel. The black (red) and green (blue) dots represent the measured QBERx (QBERz) with and without polarization feedback (PF), respectively. With the PF, QBERx=0.86%±0.17% and QBERz is 0.84%±0.13%.

Fig. 4. Secure key rates with different transmission loss. The blue line represents the simulation results based on our experimental parameters, and the red dots represent the experimental results.

Fig. 5. The way Alice sends a synchronization string is shown. The red and blue squares represent single bits of the synchronization and random string, respectively. (a) Qubit4Sync. Alice first sends a synchronous string of length L and then sends a random string for QKD. (b) Our method. Alice divided the synchronization string of length L into L single bits, and each bit is followed with M random bits to form a block. L blocks build the synchronization frame of length Nf=(M+1)L, which contains the complete synchronization string.

Fig. 6. Schematic of reverse-processing sB. Bob’s string sB is divided into L blocks of length M+1 and reshaped into an (M+1)×L matrix. Each row of the matrix reconstructs a bit string siB.

Table 1. Overview of Experimental Parameters and Performances for Different Distances^a