www.sciencemag.org/content/356/6343/1140/suppl/DC1

Supplementary Materials for

Satellite-based entanglement distribution over 1200 kilometers Juan Yin, Yuan Cao, Yu-Huai Li, Sheng-Kai Liao, Liang Zhang, Ji-Gang Ren, Wen-Qi

Cai Wei-Yue Liu, Bo Li Hui Dai, Guang-Bing Li, Qi-Ming Lu, Yun-Hong Gong, Yu Xu, Shuang-Lin Li, Feng-Zhi Li, Ya-Yun Yin, Zi-Qing Jiang, Ming Li, Jian-Jun Jia, Ge Ren, Dong He, Yi-Lin Zhou, Xiao-Xiang Zhang, Na Wang, Xiang Chang, Zhen-Cai Zhu, Nai-

Le Liu, Yu-Ao Chen, Chao-Yang Lu, Rong Shu, Cheng-Zhi Peng,* Jian-Yu Wang,* Jian-Wei Pan*

*Corresponding author. Email: pcz@ustc.edu.cn (C.-Z.P.); jywang@mail.sitp.ac.cn (J.-Y.W.);

pan@ustc.edu.cn (J.-W.P.)

Published 16 June 2017, Science 356, 1140 (2017) DOI: 10.1126/science.aan3211

This PDF file includes:

Materials and Methods Figs. S1 to S11 Table S1 References

2

Materials and Methods

This section includes detailed descriptions of the payloads in the satellite, the receiving

ground stations, the polarization compensation method, and the relevant supporting data.

1. Payloads in the satellite

The Micius satellite is double-decker designed (Fig. S1A). The payloads for the

entanglement distribution experiment are composed of a spaceborn entangled-photon

source (SEPS), two optical transmitters (the upper layer of the satellite), an experimental

control processor, and two acquiring, pointing and tracking (APT) control boxes (the

lower layer of the satellite). Here we introduce three payloads specifically designed for

the entanglement distribution, one SEPS (Fig. S1B) and two optical transmitters (Fig.

S1C, Fig. S1D).

1.1. Spaceborn entangled-photon source

The SEPS is an opto-mechatronics integration payload with the envelope of 430 mm ×

355 mm × 150 mm and the total weight of 23.8 kg. The optical elements are mounted

and glued on the both sides of a base board with thickness of 40 mm. The base board is

made of titanium alloy owing to its good balance between rigidity, thermal expansion and

density. The left panel illustrate the upper side of the setup (Fig. S2A), which can

generate entangled photon pairs. The bottom side in the right panel (Fig. S2B) contains

two reference lasers with wavelength around 810 nm, which can be used as a reference in

polarization control process and test the freespace link.

In order to achieve an optimal stability during the satellite launch and in-orbit operations,

the most sensitive structure of the setup, the Sagnac interferometer, is integrated to a

palm-sized invar material plate with a thickness of 15 mm and thermo-insulated

embedded to the titanium plate. With a confocal design, the input and output beams of

the Sagnac interferometer are collimated, which relaxes the requirement of mounting

accuracy for the optical elements. In addition, two piezo steering mirrors (PI) are used to

correct the pointing offset of the beam. To prolong the life of the source, a second pump

diode with polarization V is used as a backup. The backup pump laser beam is combined

with the other one by a polarizing beam splitter (PBS). In the development process, the

3

Sagnac interferometer module has passed a series of space environment adaptability tests,

such as the thermal-vacuum and vibration test, which are helpful to release

thermodynamic stress beforehand and enhance the system stability.

The SEPS are guided to two optical transmitters through two SMFs with lengths of 280

mm and 410 mm, respectively. After a 5× beam expander (BE), a mirror is placed in the

edge of the beam to sample entangled photons and the reference laser by 1% (Fig. S3).

An integrated BB84 receiving module, consisting of two wollaston prisms and one beam

splitter (BS), formed a random measurement of four polarizations (0, 90, 45 and 135

degree). Detector 1~4 are photodiodes for the energy detection, which work at avalanche

mode to detect entangled photons and work at linear mode to detect the reference laser.

Through the 1% sampling in both entangled-photons transmitters, we can estimate that

the source brightness is ~5.9 MHz. By rotating the HWP in the transmitter 2, we scan the

associated curve and get the visibility of better than 0.91 (Fig. 2B). Remarkably, two days

after the launch, we tested the SEPS which not only survived from the rocket acceleration

but also showed a counting rate drops only by 20%, which can be easily recovered by

adjust the PIs.

1.2. The transmitters for the entangled photon pairs

In Micius satellite, two transmitters, transmitter 1 and transmitter 2, are utilized to

distribute the entangled photon pairs to two separate ground stations simultaneously.

Both transmitters consist of a telescope and an optical box. An off-axis telescope design

is used to reduce the emission loss in transmitter 2. Each optical box (Fig. S4) consists of

a motorized wave-plates combination for polarization correction, an integrated receiving

module for sampling measurement, and the fine tracking system. Using the reference

laser, the tracking system can be self-calibrated in orbit.

2. Ground stations in Nanshan, Delingha and Lijiang

For the mission of entanglement distribution, three ground stations are cooperating with

the satellite, located in Delingha, Urumqi, and Lijiang (Fig. S5). The distance between

Delingha and Lijiang (Nanshan) is 1203 km (1120 km).

Two new telescopes (with a diameter of 1.2 m) are built in Nanshan and Delingha

specifically for the entanglement distribution experiments (Fig. S6A). All optical

4

elements in these two telescopes are polarization maintaining. The measurement boxes

are installed on one of the rotating arms and rotate along with the telescopes. In Lijiang,

we adopt the original telescope with a large diameter of 1.8 m and modified it for the

expeirment (Fig. S6B). The details of the measurement box are shown in Fig. S6C. The

fast steering mirror (FSM) and the camera construct a close-loop fine tracking system.

The 850 nm and 532 nm photons are coupled into multi-mode fibers with 320 μm core

for the synchronization. Together with the Pockel Cell, an integrated 810 nm module

with PBS inside achieve a random polarization analysis of signal photons. For Bell test,

we use quantum random number generators (RNG), which are Quantis-OEM components

from ID Quantique (http://www.idquantique.com/wordpress/wp-content/uploads/quantis-

oem-specs.pdf).

3. The acquiring, pointing and tracking system

The Micius satellite need to establish two optical downlinks simultaneously. The

cascaded multi-stage close-loop APT system is employed in both transmitters. For the

transmitter 1, the satellite attitude combined with a two-axis turnable mirror (with

rotation range of 10° in azimuth and elevation) realizes its coarse pointing. Different from

the transmitter 1, the transmitter 2 performs coarse pointing only via its two-dimensional

rotatable telescope with a turning range of ±90° in azimuth and −30°~70° in elevation.

In both transmitters, the fine tracking is realized by a FSM driven by piezo ceramics

(tracking range of 1.6 mrad). Detailed APT parameters are shown in Table S1.

For each of two optical downlink channels, according to the orbit prediction or GPS real-

time calculation, the ground station points the satellite by its 671 nm beacon laser with a

divergence angle of ~1 mrad. The coarse camera in the satellite detects the 671nm beacon

laser to measure the tracking error. With the feedback control of the two-axis turnable

mirror in the transmitter 1 (or the two-dimensional rotatable telescope in the transmitter 2)

and the camera, the coarse tracking error is less than 10 μrad, which is much smaller than

the camera’s field of view. As a subsequent step, the fine close-loop tracking error is

below 2 μrad by utilizing the FSM and the camera. Simultaneously, the transmitter 1 (or

the transmitter 2) points a beacon laser with wavelength of 532 nm and divergence angle

of 1.25 mrad to the ground station 1 (or the ground station 2). With a similar cascaded

5

multi-stage APT technique, the ground stations correct its pointing direction with an error

of 1~2 μrad. Finally, we successfully establish two downlink channels in a single pass of

the satellite. The typical orbital parameters between Nanshan and Delingha are shown in

Fig. S7 and the corresponding attenuations are from 63 dB to 78 dB.

4. Polarization compensation

In the two-downlink entanglement distribution experiment, a diagram of the overall

transmission process of polarization-entangled photon pairs from the generation to the

detection is shown as Fig. S8. For such a complex system, before performing the polarization

analysis, we need to correct the photons’ polarization state to its original state generated from

the source. Here, for convenience, we define four reference systems to investigate the

changes of photon’s polarization. They are the reference systems (FS) of the spaceborn

entangled-photon source, the spaceborn optical transmitter, the ground telescope, and the

ground polarization measurement module. All the polarization corrections realized

automatically according to the satellite orbit prediction data sent to satellite and ground

stations before performing the experiment.

4.1. Polarization correction against the SMFs

The SMF changes the polarization state of transmitted photons owing to the birefringent

effect. Here, we employ two automatic polarization correction systems to undo the

unknown unitary transformations applied by the SMFs for the two transmitters

respectively.

The automatic polarization compensation process can be divided to two steps. First,

similar to the process tomography, two probe state |𝐻⟩ and |+⟩ are prepared in the SEPS

using the reference lasers. The 1% sampling of reference light is used for tomography

measurement, carried out on the states after the fiber by the polarization analysis module

together with the wave-plates combination. The unitary transformation is then uniquely

determined. With the online computing and analysis by the spaceborn experimental

control processor, the angles of the motorized wave-plates combination that can construct

the corresponding inverse transformation are calculated. Second, the compensate angles

are given to the motorized stages to implement the polarization compensation on the

entangled photons.

6

The fibers are quite stable in orbit benefited from the consolidating and stress relieving

before the launch. However, they were greatly disturbed during the launch owing to the

vibration and the change of environment. The polarization correction process is carried

out once after the launch. Then the probe states maintain after transmitting through the

fibers with fidelity over 99.7% at least for several weeks.

4.2. Polarization correction against telescope rotation

In most cases, the polarization state changes over time due to the two-dimensional

rotation of the telescope. Follow the telescope azimuth or elevation rotation, a pair of

mirrors changes its position (Fig. S9). The green mirror can be rotated around the dashed

line. When the green mirror rotates 𝜃 around the dashed line, the polarization direction of

the outgoing photon rotates −𝜃. The corresponding matrix is R(−θ). Here, R(θ) =

(cos θ − sin θsin θ cos θ

). We define the pointing angle of the telescope i at time t are θiA(t) and

θiE(t). Then we get Ui(t) = R(−θiE(t))R(−θiA(t)) = R(−θiA(t) − θiE(t)).

From the spaceborn entangled-photon source FS to the satellite transmitter FS—

For the transmitter 1, the satellite attitude combined with a two-axis turnable mirror

realizes its coarse pointing. Only fixed rotation transform R(θ1), determined by the

telescope structure, needs to be compensated. For the transmitter 2, in addition to the

fixed rotation R(θ2), a real-time compensation U1(t) is realized through the HWP on the

satellite for the transmitter 2.

4.3. Polarization correction against the satellite rotation

From the satellite transmitter FS to the ground station FS—

When the satellite is passing over the ground station, the ground telescope and the

satellite’s optical transmitter need to be aligned with each other continuously (35). The

rotation of the satellite around the alignment axis will cause the rotation of photon

polarization direction. We define the rotation angle to θK at the time t. The corresponding

transformation matrix is U𝐾(t) = R(−θ𝐾).

4.4. Polarization correction against polarization non-maintaining components

From the ground station FS to the ground polarization measurement module FS—

7

The optical components in receiving telescope in Lijiang will introduce a phase delay

between the s and p polarization component. The entire optical path of telescope can be

divided into three sections by two rotating axis. We define the introduced phases in these

three sections as φ1, φ2 and φ3 respectively. The corresponding transformation matrix is:

Ub(t) = P(φ3)R(θbA(t))P(φ2)R(θbE(t))P(φ1). Here, P(φ) = (1 00 eiφ) .

In the ground station, we solve the inverse matrices of the above matrices to realize the

correction on polarization state. A motorized half- and quarter-wave plates combination

is utilized in Lijiang for the polarization correction against both the kinematical reference

system and the phase shifts in the optical components.

In Delingha and Nanshan, the telescopes are specially coated and measured without the

unwanted phase shift. The polarization measurement module is mounted on the azimuth

axis of the receiving telescope. Thus there is only one rotational degree of freedom

θaE(t) between the polarization measurement module and the receiving telescope. The

transformation matrix is simplified to Ua(t) = R(−θaE(t)) and the wave-plates

combination can be reduced to only one half-wave plate.

5. Far-field divergence angle measured in orbit

The beam divergences of two transmitters in the satellite are designed to be about 10 µrad.

Before launch, the beam divergence of the transmitter 1 (transmitter 2) was about 11

µrad × 9 µrad (10 µrad × 12 µrad) (Fig. S10A, Fig. S10C), measured through a beam

analyzer and a collimator in a vacuum tank. By setting different tracking points in the

satellite and measuring the corresponding receiving count rates on the earth, we measured

the divergence angle in orbit (Fig. S10B, Fig. S10D). The brightness indicates the

receiving count rates and the X/Y-axis indicates the beam optical axis deviation. Both the

measured far-field beam divergences of two transmitters are 10 µrad, which is as

expected.

6. Synchronization system

Quantum entanglement distribution experiment uses a 850 nm laser (pulse width less than

1 ns) for synchronization, which is split into two parts transmitted to two ground stations

respectively. The two ground stations detect the synchronization pulses by single-photon

8

detectors, and record their arrival time by the time-to-digital convertor (TDC). The data

were recorded by local TDC system of each ground stations. All the TDC systems are

synchronized via GPS signals. As the frequency of the laser is relatively stable, a least-

squares method is used to fit the selected pulses, which can eliminate the time jitter of

synchronization detectors. As shown in Fig. S11, the time synchronization accuracy of

entangled photon pairs is ~0.77 ns (1σ).

9

Fig. S1

The pictures of payloads in the satellite. (A) The payload layout. (B) The SPES in

mechanics test. (C) The transmitter 1 with a diameter of 300 mm. (D) The transmitter 2 with a diameter of 180 mm.

10

Fig. S2

Schematic diagram of the SEPS. The optical elements are mounted and glued on the both

side of a titanium alloy base board. (A) The upper side generates entangled photon pairs.

(B) The bottom side offers reference lasers for polarization control process and freespace

channel testing. Two lasers with wavelength around 810 nm are polarized at 0 and 45-

degree, respectively. Both laser beams are split on a beam splitter (BS) and combined

with the entangled-photon beams by two pairs of prism. HWP, half-wave plate; QWP,

quarter-wave plate; BS, beam splitter; PBS, polarizing beam splitter; DM, dichroic

mirror; PI, piezo steering mirror; PPKTP, periodically poled KTiOPO4.

A B

11

Fig. S3

Setup for the on-satellite tests. The polarization compensation and entanglement fidelity

tests were realized by sampling 1% of the photons in both paths. WP, wollaston prism;

HWP, half-wave plate; QWP, quarter-wave plate; BS, beam splitter; IF, interference filter.

12

Fig. S4

Top side view of entangled-photons transmitter optics head. The collimated beam from

SPES, passes through a motorized wave-plates combination, a beam expander, and then

is combined with the 850 nm synchronization laser by a DM. 1% of the main beam is

reflected by a sampling mirror to a BB84 receiving module. FSM: fast steering mirror. (A)

Top side view of transmitter 1’s optics head. (B) Top side view of transmitter 2’s optics

head.

13

Fig. S5

Geographic map of the ground stations.

14

Fig. S6

Telescopes and measurement box at ground station. (A) Newly-built telescope in

Nanshan and Delingha. (B) Telescope in Lijiang. (C) Optical measurement box.

A B

C

15

Fig. S7

Distances from satellite to Nanshan (Delingha) and the measured attenuations. (A) A

typical two-downlink trial from satellite to Nanshan, and to Delingha, lasts about 350

seconds (over 10 degree elevation angle for both ground stations) in a single pass of the

satellite. The distance from satellite to Nanshan (Delingha) is about 585 km (930 km) to

1700 km. The overall length of the two-downlink channel varies from 1580 km to 3150 km. (B) The measured satellite-to-ground two-downlink channel attenuation.

16

Fig. S8

The process of polarization-entangled photon pairs transmission and polarization

compensation.

17

Fig. S9

Polarization rotation induced by a pair of mirrors.

18

Fig. S10

Far-field beam divergence measurements. Picture A (B) is the result of transmitter 1 in

the vacuum tank (orbit); picture C (D) is the result of transmitter 2 in the vacuum tank (orbit).

A

B

B

C D

19

Fig. S11

Time synchronization analysis. Synchronization accuracy of 𝛔 = 𝟎. 𝟕𝟕 ns was observed,

𝛔 is standard deviation of Gaussian fit (solid line).

20

Table S1. Performance of the APT system

Components Transmitter 1 Transmitter 2 Receiver

Coarse

pointing

mechanism

Type Two-axis gimbal

mirror

Two-axis turntable Two-axis turntable

Tracking

range

Azimuth:±5°

Elevation:±5°

Azimuth: ±90°

Elevation:-30~75°

Azimuth: ±270°

Elevation:-3°~95°

Coarse

camera

Type CMOS CMOS CCD

Field of view

(FOV)

2.3×2.3° 2.3×2.3° 0.33×0.33°

Size & Frame 512×512 & 40 Hz 512×512 & 40 Hz 512×512 & 56 Hz

Fine tracking

mechanism

Type PZT FSM PZT FSM PZT FSM

Range ±5 mrad ±5 mrad ±17.5 mrad

Fine tracking

camera

Type CMOS CMOS CCD

FOV 0.64×0.64 mrad 0.64×0.64 mrad 1.3×1.3 mrad

Size & Frame 60×60 &2 KHz 60×60 &2 KHz 128×128 & 212 Hz

Beacon laser Power 110 mW 50 mW 2.3 W

Wavelength 532 nm 532 nm 671 nm

Divergence 1.2 mrad 0.65 mrad 1.5 mrad

Tracking error 0.5 μrad ×0.8 μrad 0.5 μrad ×0.6 μrad 1.4 μrad ×1.8 μrad

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