Quantum entanglement enables tasks not possible in classical physics. Many quantum communication protocols1 require the distribution of entangled states between distant parties. Here, we experimentally demonstrate the successful transmission of an entangled photon pair over a 144 km free-space link. The received entangled states have excellent, noise-limited fidelity, even though they are exposed to extreme attenuation dominated by turbulent atmospheric effects. The total channel loss of 64 dB corresponds to the estimated attenuation regime for a two-photon satellite communication scenario. We confirm that the received two-photon states are still highly entangled by violating the Clauser–Horne–Shimony–Holt inequality by more than five standard deviations. From a fundamental point of view, our results show that the photons are subject to virtually no decoherence during their 0.5-ms-long flight through air, which is encouraging for future worldwide quantum communication scenarios.
Entanglement is at the heart of many peculiarities encountered in quantum mechanics and has enabled many groundbreaking tests on the fundamentals of nature. Entangled photons are ideal tools to investigate the laws of quantum mechanics over long distances and timescales because they are not subject to decoherence. Furthermore, photons can be easily generated, manipulated and transmitted over large distances through optical fibres or free-space links. As the maximal distance for the distribution of quantum entanglement in optical fibres is limited to the order2,3,4,5 of ∼100 km with state-of-the-art technology, the most promising option for testing quantum entanglement on a global scale at present is free-space transmission, ultimately using satellites and ground stations6.
In recent years, various free-space quantum communication experiments with weak coherent laser pulses7,8,9,10,11 and entangled photons12,13,14,15 have been carried out on ever larger distance scales and with increasing bit rates. So far, the most advanced test bed for free-space distribution of entanglement is a 144 km free-space link between two Canary Islands, where the successful transmission of one photon of an entangled pair was recently achieved16. In the present experiment, we demonstrate a fundamentally more interesting scenario by sending both photons of an entangled pair over this free-space channel. By violating a Clauser–Horne–Shimony–Holt (CHSH) Bell inequality17, we find that entanglement is highly stable over long time spans—the photon-pair flight time of ∼0.5 ms is the longest lifetime of photonic Bell states reported so far, almost twice as long as the previous high4,5 of ∼250 μs.
The achieved noise-limited fidelity paves the way for free-space implementations of quantum communication protocols that require the transmission of two photons, such as, quantum dense coding18, entanglement purification19, quantum teleportation20 and quantum key distribution without a shared reference frame21. From a technological perspective, the overall two-photon loss bridged in our experiment is significantly higher than the current 40 dB limit22 for alternative set-ups relying on weak coherent laser pulses. The attenuation of 64 dB corresponds to the expected attenuation for a satellite scenario with two ground stations6, proving the feasibility of quantum communication on a global scale.
The experiment was conducted between La Palma and Tenerife, two Canary Islands situated in the Atlantic Ocean off the West African coast. An overview of the experimental scheme is shown in Fig. 1. At the transmitter station at La Palma, photon pairs at a wavelength of 810 nm and a bandwidth (full-width at half-maximum) of 0.6 nm were generated in a 10-mm-long, periodically poled KTiOPO4 crystal that was bidirectionally pumped by a grating-stabilized 405 nm diode laser. The photon pairs were coherently combined in a polarization Sagnac interferometer23,24 and emitted in the maximally entangled state:
where H/V denote the photons polarization state (horizontal/vertical) and ϕ is an unknown phase.
At 20 mW of pump power, the source produced ∼107 photon pairs per second of which ∼3.3×106 single photons per second and ∼106 pairs per second were detected locally. These pairs were coupled into single-mode fibres with a length difference of 10 m, which introduced a time delay of Δt=50 ns between the two photons. The two photons were then transmitted by two telescopes mounted on a motorized platform and a common receiver telescope—the European Space Agency’s Optical Ground Station (OGS) located on Tenerife. The transmitters consisted of single-mode fibre couplers and f/4 best form lenses (focal length f=280 mm) that had a lateral separation of 10 cm. To actively compensate the transmitter platform and receiver pointing directions for drifts of the optical path through the time-dependent atmosphere, a bidirectional closed-loop tracking mechanism was used: at the transmitter platform, the virtual position of a 532 nm beacon laser attached to the OGS was monitored in the focus of a third telescope by a CCD (charge-coupled device) camera. Likewise, the OGS monitored the position of a beacon laser mounted at the transmitter (see Fig. 1 and ref. 11 for details).
At the OGS, the incoming photons were collected by a 1 m mirror (f=38 m). To ensure that turbulence-induced beam wander did not divert the beam off the detectors, the photons were collimated (f=400 mm) before they were guided to a polarization analysis module. Here, a symmetric 50/50 beam splitter directed impinging photons randomly to one of two polarization analysers (A, B), each consisting of a half-wave plate (HWPA, HWPB), mounted in a motorized rotation stage, and a polarizing beam splitter (PBS). The polarized light was then refocused (f=50 mm) onto four single-photon avalanche diodes (SPADs). A time-stamping unit recorded clicks in the four SPADs and encoded and stored their respective channel number and arrival time relative to a common internal clock with 156 ps resolution. Figure 2a shows the cross-correlations of these time-stamps for two exemplary measurements. One can clearly identify the two coincidence peaks at ±50 ns around zero delay, which corresponds to the fibre delay Δt introduced at the transmitter. The average width (full-width at half-maximum) of the coincidence peaks was 560 ps, dominated by the timing jitter of the SPADs. To obtain the number of coincident photons, we summed up the number of correlations in a time window of 1.25 ns centred at the coincidence peak positions (Fig. 2b).
As a witness for the presence of entanglement between the received photons, we tested the CHSH Bell inequality17:
where E(θA,θB)=(CTT(θA, θB)+CRR(θA,θB)−CTR(θA,θB)−CRT(θA, θB))/N is the normalized correlation value of polarization measurement results on photon pairs. Ca b(θA, θB) is the number of coincidences measured between detectors at the (T/R) output ports (Fig. 1) of the polarization analysers A and B set to angles (θA, θB) and N is the sum of these coincidences. Whenever S exceeds the classical bound S>2, the polarization correlations cannot be explained by local hidden variable models17. For the maximally entangled state |ψ−〉, quantum theory predicts a value of for the settings (α,β,α′,β′)=(0,π/8,π/4,3π/8).
The detection module in our experiment enabled us to directly measure the expectation values E(θA,θB) in equation (2) with four different sets of angles of HWPA and HWPB (Table 1). We first aligned the system to obtain a |ψ−〉 state at the receiver (see details in the Methods section). For each setting (θA,θB), we repeatedly accumulated data for typically 900 s, which eventually amounted to a total of 10,800 s acquired in three consecutive nights. Each detector registered an intrinsic dark count rate of ∼200 s−1, and additionally background light of ∼200 s−1. In total, we received an average signal of 2,500 single photons per second and 0.071 photon pairs per second. Even though the final single-photon-to-coincidence ratio at the receiver was just 1.7×10−5, the coincidence signal-to-noise ratio was as high as ∼15:1. Compared with the count rates detected at the source, the single-photon attenuation was 34 dB, of which 2 dB was due to the lower efficiency of the detectors used at the receiver (∼25%) compared with those at the source (∼40%). The measured total photon-pair loss was 71 dB, of which 3 dB was contributed by the beam splitter in the receiver module. The average net attenuation experienced by single photons along the free-space link was therefore 32 dB and the photon-pair attenuation of 64 dB was exactly twice as large, which results from the fact that a pair of photons has double the extinction of a single photon transiting the path. As we have previously ruled out any other adverse effects such as depolarization or timing jitter, which might occur between photons in independent channels16, we can compare our results to a scenario with two separate free-space links. A detailed analysis22 of the error sources in our system enabled us to estimate the expected background and multiphoton-pair emissions limited quantum visibility to 94.4%. Combined with the source visibility (99.2%) and the polarization contrast of the detection module (99.5%), the upper bound for the overall system visibility was Vtot=93.2%. As the observed CHSH Bell parameter is connected to the set-up visibility through Smax=Vtot×SQM, this implies a maximum achievable Bell parameter of Smax=2.636.
The accumulated coincident events for the different detector pairs yielded the correlation values shown in Table 1. According to equation (2), we measured a CHSH Bell parameter Sexp of:
which is in excellent agreement with our estimate Smax. Our result violates the CHSH inequality by 5.4 standard deviations and convincingly proves the successful transmission of entanglement. The fact that Sexp is so close to Smax shows that the fidelity between the transmitted and received entangled states was essentially noise-limited. Therefore, the entanglement was not affected by decoherence, even though the photons were subject to extreme attenuation that was dominated by turbulent atmospheric fluctuation16.
Note that our set-up contains some of the basic building blocks of a quantum communication system. However, the set-up could not be used to carry out an actual quantum key distribution experiment25 owing to the lack of a second independent analyser module. In addition, a fully-fledged implementation would have required classical post-processing protocols, that is, error correction and privacy amplification. Nevertheless, from the measured Sexp, we can infer a qubit error ratio of 3.85±2.2%. Further note that the photon-pair creation rate of ∼106 pairs per second at the source is necessary6 for the long-distance distribution of quantum entanglement in the demonstrated high-attenuation regime. The compact entangled photon source, being pumped by a low-power diode laser, can readily be integrated into a satellite-borne photonic terminal, which was previously14,16 not the case. We expect that this will enable fundamental tests of the laws of quantum mechanics on a global scale26.
Before measuring the polarization correlations for equation (2), we had to establish a common polarization reference frame between the individual transmitters and the receiver and to adjust the phase ϕ of the quantum state in equation (1) such that the detected coincidence signature was consistent with one of the desired Bell states. For the polarization compensation, we used an auxiliary 808 nm laser diode, which was directed at the entangled source such that linearly polarized light was coupled into the fibres at a well-defined single-photon level (Fig. 1). We set HWPA and HWPB in the detection module to (0∘, 0∘), measuring in the |H/V 〉 basis, and manually adjusted the fibre polarization controllers at the source to maximize the single-photon polarization visibility VH/V in the remote detectors. The achieved visibility in this basis was typically 95%.
Once the linear polarization was set, the auxiliary laser was switched off and ϕ was tuned using entangled photons. The visibility V± in the |±〉 basis depends on ϕ as V±=V0cos(ϕ). To determine the relation between ϕ and the wave plates controlling the pump laser in the source (HWPS, QWPS), we set HWPA and HWPB in the detection module to (π/8, π/8), measured V± for three different settings of HWPS and QWPS in the equatorial plane of the Poincaré sphere that represents the pump laser polarization (see refs 23, 24) and then numerically fitted a cosine function to the obtained data points. The fitted two-photon fringes in Fig. 3 correspond to a visibility of V0=84±2.4%. From this fit, we deduced the wave-plate settings to obtain either a |ψ−〉 or a |ψ+〉 state in the detection module. This procedure was repeated each night at the beginning of a measurement.
We obtained the coincidence measurements in Fig. 2 after we prepared |ψ−〉 and |ψ+〉 states using this method. The measured respective visibility of V±=80±7.6% and V±=90±5.5% at the receiver is depicted in Fig. 3. As the linear polarization of the individual photons could be adjusted arbitrarily at the source, we were thus able to prepare, transmit and distinguish any of the four Bell states at the receiver.
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We are grateful to H. Weinfurter, J. G. Rarity, T. Schmitt-Manderbach, C. Barbieri, F. Sanchez, A. Alonso, J. Perdigues and Z. Sodnik, T. Augusteijn and the staff of the Nordic Optical Telescope in La Palma for their support at the trial sites. This work was supported by ESA under the General Studies Programme (No. 18805/04/NL/HE), the European Commission through Project QAP (No. 015846), the DTO-Funded US Army Research Office, the Austrian Science Foundation (FWF) under project number SFB1520 and the ASAP-Programme of the Austrian Space Agency (FFG).
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Fedrizzi, A., Ursin, R., Herbst, T. et al. High-fidelity transmission of entanglement over a high-loss free-space channel. Nature Phys 5, 389–392 (2009). https://doi.org/10.1038/nphys1255
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