Satellite-based entanglement distribution over 1200 kilometers

Limitations on entanglement distribution

So far, entanglement distribution has only been achieved at a physical separation up to ~100 km (10) and is mainly limited by the photon loss in the channel (optical fibers or terrestrial free space), which normally scales exponentially with the channel length. For example, through bidirectional distribution of an entangled source of photon pairs with a 10-MHz count rate directly through two 600-km telecommunication fibers with a loss of 0.16 dB/km, eventually one would only obtain 10⁻¹² two-photon coincidence events per second. When the transmitted photons are attenuated to a level comparable to the dark counts of the single-photon detectors, the entanglement cannot be established because of the low signal-to-noise ratio. To improve the signal-to-noise ratio, the entangled photons in the channel cannot simply be amplified because of the quantum noncloning theorem (11), but radically new methods to reduce the link attenuation must be developed.

One solution to improve the distribution is the protocol of quantum repeaters (12) that divide the whole transmission line into smaller segments and combine the functionalities of entanglement swapping (13), entanglement purification (14), and quantum storage (15). There has been considerable progress in the demonstrations of these building blocks (16–18) and proof-of-principle quantum repeater nodes (19, 20). However, the practical usefulness of the quantum repeaters is still hindered by the challenges of simultaneously realizing and integrating all the key capabilities, including, most importantly, long storage time and high retrieval efficiency (21).

Satellite-based entanglement distribution

Another approach to global-scale quantum networks is making use of satellite- and space-based technologies. A satellite can conveniently cover two distant locations on Earth separated by thousands of kilometers. The key advantage of this approach is that the photon loss and turbulence predominantly occur in the lower ~10 km of the atmosphere, and most of the photons’ transmission path is virtually in vacuum, with almost zero absorption and decoherence. Previously, ground-based feasibility studies have demonstrated bidirectional distribution of entangled photon pairs through a two-link terrestrial free-space channel—with violations of Bell inequality—over distances of 600 m (22); 13 km, which goes beyond the effective atmospheric thickness (23); and 102 km with an ~80-dB effective channel loss, comparable to that of a satellite-to-ground two-downlink channel (10). In addition, quantum communications on moving platforms in a high-loss regime and under turbulent conditions were also tested (24, 25). After these feasibility studies, a satellite dedicated for quantum science experiments, Micius [see the supplementary materials (26)], was developed and launched from Jiuquan, China, to an altitude of ~500 km.

For the mission of entanglement distribution, three ground stations are cooperating with the satellite, located in Delingha in Qinghai (37°22′44.43′′N, 97°43′37.01′′E; altitude, 3153 m); Nanshan in Urumqi, Xinjiang (43°28′31.66′′N, 87°10′36.07′′E; altitude, 2028 m); and Gaomeigu Observatory in Lijiang, Yunnan (26°41′38.15′′N, 100°1′45.55′′E; altitude, 3233 m). The physical distance between Delingha and Lijiang (Nanshan) is 1203 km (1120 km). The separation between the orbiting satellite and these ground stations varies from 500 to 2000 km. The effective laboratory space is thus greatly increased and provides a new platform for quantum networks, as well as for probing the validity of quantum mechanics.

By developing an ultrabright spaceborne two-photon entanglement source and high-precision acquiring, pointing, and tracking (APT) technology, we established entanglement between two single photons separated by 1203 km, with an average two-photon count rate of 1.1 Hz and state fidelity of 0.869 ± 0.085. Using the distributed entangled photons, we performed the Bell test at spacelike separation and without the locality and the freedom-of-choice loopholes.

Spaceborne entangled photons

In our design of a spaceborne entangled-photon source (Fig. 1A), a continuous-wave laser diode with a central wavelength of 405 nm and a linewidth of ~160 MHz is used to pump a periodically poled KTiOPO₄ crystal inside a Sagnac interferometer. The pump laser, split by a polarizing beam splitter, passes through the nonlinear crystal in the clockwise and anticlockwise directions simultaneously, which produces down-converted photon pairs at a wavelength of ~810 nm in polarization-entangled states close to the form , where and denote the horizontal and vertical polarization states, respectively, and the subscripts 1 and 2 denote the two output spatial modes. This source is robust against various vibration, temperature, and electromagnetic conditions (26). After launch, the source brightness and fidelity were tested by sampling ~1% of each path of the entangled photon pairs for on-satellite analysis (Fig. 1B). Under a pump power of ~30 mW, the source emits 5.9 million entangled photon pairs per second, with a state fidelity of 0.907 ± 0.007.

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Establishing a space-to-ground two-downlink channel

As the entangled photons propagate from the satellite through the atmosphere to the two ground stations, each with a travel distance of 500 to 2000 km, several effects contribute to channel loss, including beam diffraction, pointing error, atmospheric turbulence, and absorption. Because the entangled photons cannot be amplified as classical signals, a robust and efficient satellite-to-ground entanglement distribution places more stringent requirements on the link efficiency than conventional satellite-based classical communications do. In particular, a satellite payload with two telescopes capable of establishing two independent satellite-to-ground quantum links simultaneously is required.

To optimize the link efficiency, we combined a narrow beam divergence with a high-bandwidth and high-precision APT technique. The two entangled beams were sent out with a near-diffraction-limited far-field divergence of ~10 μrad by two Cassegrain telescopes with apertures of 300 and 180 mm (Fig. 2A), which have been optimized to eliminate chromatic and spherical abbreviations at a wavelength of ~810 nm. The overall optical efficiencies of the two telescopes are 45 to 55%. At the Delingha, Lijiang, and Nanshan stations, the receiving telescopes have diameters of 1200, 1800, and 1200 mm, respectively. Our experiment has achieved entanglement distribution both between Delingha and Lijiang and between Delingha and Nanshan (26).

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We designed cascaded multistage closed-loop APT systems in both the transmitters (Fig. 2A) and receivers (Fig. 2B). The transmitters use green (~532 nm) beacon lasers, whereas the receivers use red (~671 nm) beacon lasers, pointing to each other with a divergence of ~1.2 mrad. The coarse pointing stages consist of a two-axis turntable or gimbal mirror and wide field-of-view cameras, and they achieve an accuracy better than 50 μrad. Further, the fine pointing stages with fast-steering mirrors and high-speed cameras reliably lock the remote telescopes by a feedback closed loop with a measured accuracy of 0.41 μrad for both the x and y axes (Fig. 2C), much smaller than the beam divergence (26). The APT systems are started when the satellite reaches a 5° elevation angle, and the measurement begins when it reaches a 10° elevation angle.

The motion of the satellite relative to the ground induces a drift in the arrival time and polarization rotation observed by the receivers. We kept track of the relative motion between the transmitters and the receivers, as well as all the optical elements in the optical paths, to calculate the polarization rotation angle offset and phase shift. Using a combination of motorized wave plates (two quarter-wave plates and one half-wave plate) for dynamical polarization compensation (26), we were able to recover the polarization contrast to 80:1. Synchronization of two ground stations was done with a 100-kHz pulsed laser, sent from the satellite and in good co-alignment with the signal photons. A synchronization jitter of 0.77 ns was obtained, which was used to tag the received signals and perform coincidence detection within a 2.5-ns time window. In addition to the temporal filtering, we placed 20-nm bandwidth filters in the receiving telescope to reduce the background noise. In our experiment, depending on the position of the Moon, the background noise ranged from 500 to 2000 counts/s in each detector.

The satellite flies along a sun-synchronous orbit and comes into both Delingha’s and Lijiang’s views once every night, starting at around 1:30 AM Beijing time and lasting for a duration of ~275 s. Figure 3A plots the physical distances from the satellite to Delingha and Lijiang during one orbit, together with the summed channel length of the two downlinks. Using a reference laser (26) on the satellite, we measured in real time the overall two-downlink channel attenuation, which varies from 64 to 82 dB (Fig. 3B). A slight asymmetry is evident in the attenuation curve—when the satellite moves closer to Lijiang, the link efficiency is higher, which is because the Lijiang station has a larger-aperture telescope. We observed an average two-photon count rate of 1.1 Hz, with a signal-to-noise ratio of ~8:1.

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Compared with the previous method of entanglement distribution by direct transmission of the same two-photon source—using the best-performance (with a loss of 0.16 dB/km) and most common (with a loss of 0.2 dB/km) commercial telecommunication fibers, respectively—the effective link efficiency of our satellite-based approach within the 275-s coverage time is 12 and 17 orders of magnitude higher (27). The intrinsic physical loss limit of the silica optical fibers is estimated to be 0.095 to 0.13 dB/km (28). Even if such perfect optical fibers were produced in the future, our satellite-based method would still be four to eight orders of magnitude more efficient. In the future, satellites at higher orbits are expected to increase the area and time coverage.

Verifying entanglement and Bell test

The received photons were analyzed by a half-wave plate, a polarizing beam splitter, and a Pockels cell, then coupled into a multimode fiber and detected by single-photon detectors with low dark counts (<100 Hz). The Pockels cells were driven by high-voltage pulses rapidly switching between zero- and half-wave voltages, controlled by fast (4 megabits/s) random numbers. Such a setting allows measurements of polarization at the basis of . To verify whether the two photons, after traveling the overall distance ranging from 1600 to 2400 km, were still entangled, we analyzed their polarizations in the and bases. We obtained 134 coincidence counts—raw data without subtracting background noise—during an effective time of 250 s in satellite-orbit shadow time (Fig. 4). We found that, in good agreement with the state , the and populations dominate in the basis (Fig. 4A). Further, the coherence of the state is evident in Fig. 4B, where the measured and counts dominate over and at a ratio of 16:1. From these measurements, we can estimate the state fidelity [defined as the wave function overlap of the experimentally obtained states with the ideal (29)] of the two photons distributed over 1203 km: F ≥ 0.87 ± 0.09, which is well above the threshold for both confirming the two-particle entanglement and violating Bell inequalities.

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We used the distributed entangled photons for the Bell test with the Clauser-Horne-Shimony-Holt (CHSH)–type inequality (30), which is given byS = |E(ϕ₁,ϕ₂) – E(ϕ₁,ϕ₂′) + E(ϕ₁′,ϕ₂) + E(ϕ₁′,ϕ₂′)| ≤ 2where E(ϕ₁,ϕ₂), E(ϕ₁,ϕ₂′), and so forth are the joint correlations at the two remote locations with respective measurement angles of (ϕ₁,ϕ₂), (ϕ₁,ϕ₂′), and so forth. The angles are randomly selected among (0, π/8), (0, 3π/8), (π/4, π/8), and (π/4, 3π/8), quickly enough to close the locality (31) and freedom-of-choice loopholes (Fig. 5A). We ran 1167 trials of the Bell test during an effective time of 1059 s. The data observed in the four settings are summarized in Fig. 5B, from which we found S = 2.37 ± 0.09, with a violation of the CHSH-type Bell inequality S ≤ 2 by four standard deviations. The result again confirms the nonlocal feature of entanglement and excludes the models of reality that rest on the notions of locality and realism—on a previously unattained scale of thousands of kilometers.

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