Long-Distance Free-Space Measurement-Device-Independent Quantum Key Distribution

Measurement-device-independent quantum key distribution (MDI-QKD), based on two-photon interference, is immune to all attacks against the detection system and allows a QKD network with untrusted relays. Since the MDI-QKD protocol was proposed, fiber-based implementations aimed at longer distance, higher key rates, and network verification have been rapidly developed. However, owing to the effect of atmospheric turbulence, MDI-QKD over a free-space channel remains experimentally challenging. Herein, by developing a robust adaptive optics system, high-precision time synchronization and frequency locking between independent photon sources located far apart, we realized the first free-space MDI-QKD over a 19.2-km urban atmospheric channel, which well exceeds the effective atmospheric thickness. Our experiment takes the first step toward satellite-based MDI-QKD. Moreover, the technology developed herein opens the way to quantum experiments in free space involving long-distance interference of independent single photons.

Figure 1

Setup of free-space MDI-QKD. (a) Top view of the experimental layout at the Pudong area, Shanghai. Alice and Bob are in opposite directions from the measurement station, at distances of 7.7 and 11.5 km, respectively. (b) Arriving photon pulses interference on a fiber beam splitter (FBS) are detected by superconducting nanowire single photon detectors (SNSPDs). Before entering the FBS, a fiber polarization beam splitter (FPBS) is employed to filter the polarization, allowing about 10% to be directly measured for time synchronization. (c) A camera and a fast steering mirror (FSM) together operate as the acquiring, pointing, and tracking system. The stochastic parallel gradient descent algorithm-based AO system compensates the wave front aberration to maximize the coupling efficiency of SMFs using a DM. (d) The photon sources for MDI-QKD at Alice and Bob. A hydrogen cyanide (HCN) molecule absorption cell is employed to calibrate the wavelength of two DFB laser diodes (LDs). The optical pulses generated from LD1 are further modulated by an amplitude modulator (AM) to obtain better uniformity. An asymmetric interferometer is employed to generate pulse pairs. To ensure the relative phase between the two pulses, the interferometer is phase locked by continuous wave laser emitted from LD2 at the same wavelength as that of the signal laser. The encoding is performed by two AMs and a phase modulator (PM). Note: OS, optical switch; CIR, circulator; FM, Faraday mirror; PC, polarization controller; PS, phase shifter; PD, photodiode; DET, single photon detector; BL, beacon laser; DWDM, dense wavelength division multiplexing; ATT, attenuation.

Figure 2

Coincidence count of the HOM interference over a long-distance free-space channel. By scanning the time delay of the two detector channels, the coincidence count varies to show the visibility. With all data counted in, the visibility is $0.412\pm 0.001$, which is mainly effected by the fluctuation of channel efficiency. Further data postselecting occurs with the assistance of an additional reference laser. By ruling out pulse pairs with a different average photon number (by the threshold of 0.98), a visibility of $0.474\pm 0.010$ is obtained, which is close to the limitation of HOM interference by coherence states.

Figure 3

Results of MDI-QKD. (a) With the postselection process, $6.15\times {10}^3\mathrm{s}$ of valid time are selected from entire data of $4.8\times {10}^4\mathrm{s}$ using a threshold of $r_p>0.8$. The final key rate per pulse of $7.94\times {10}^{-8}$ (consideration finite key length) is shown as the solid circle, which is close to the simulated curve. The hollow circle represents the effective secure key rate of postselected data over entire data taking duration, i.e., $4.8\times {10}^4\mathrm{s}$, which is diminished significantly to $1.01\times {10}^{-8}$. The secure key rate without postselection is calculated as $5.93\times {10}^{-8}$ by data over $6.13\times {10}^3\mathrm{s}$, shown as the triangle. For a fair comparison, these time slots comprising four sets of continuously acquired data picked from the entire dataset have total loss and valid time similar to those of the postselected data. (b) Quantum bit error rates for each basis. QBERs for the $Z\text{−}Z$ and $X_1\text{−}{X}_1$ bases are 0.23% and 33.6%, respectively.