Abstract

The measurement of quantum signals that travel through long distances is fundamentally and technologically interesting. We present quantum-limited coherent measurements of optical signals that are sent from a satellite in geostationary Earth orbit to an optical ground station. We bound the excess noise that the quantum states could have acquired after having propagated 38,600 km through Earth’s gravitational potential, as well as its turbulent atmosphere. Our results indicate that quantum communication is feasible, in principle, in such a scenario, highlighting the possibility of a global quantum key distribution network for secure communication.

© 2017 Optical Society of America

1. INTRODUCTION

Quantum mechanics has successfully undergone a number of fundamental experimental tests since its development [13]. Still, some aspects pose both a theoretical and experimental challenge, such as the relationship of quantum mechanics and gravity [46]. Quantum-limited measurements of quantum states traveling through long distances in outer space provide both an offer to test quantum mechanics under such extreme conditions and a prerequisite for its use in quantum technology [7]. To this end, satellite quantum communication [815] promises to provide the currently missing links for global quantum key distribution (QKD). Important experiments in satellite quantum communication have been reported or are currently being devised and set up [1622].

This work presents and discusses quantum-limited measurements on optical signals sent from a geostationary satellite. We report on the first bound of the possible influence of physical effects on the quantum states traveling through Earth’s gravitational potential and evaluate its impact on quantum communication.

Optical space-to-ground experiments for long-distance classical data communication began in 1994 [23] and have since been continued with successful demonstrations of optical ground links from low Earth orbit (LEO) [24], geostationary Earth orbit (GEO) [25] and the Moon [26] (for a summary, see [27]). In parallel, free space quantum communication has progressed out of laboratories into real-world scenarios [2834]. It turns out that detecting field quadratures (continuous variables) is well suited to combat disturbances from atmospheric turbulence and stray light [3537]. Using these methods, the first implementation of an intra-urban free space quantum link using quantum coherent detection has been reported [38,39]. The advantage of stray light immunity also applies to classical coherent satellite communication [40]. The similarity between these classical and quantum technologies enables us to use the platform of a technologically mature laser communication terminal (LCT) [4143] for future quantum communication (see Fig. 1).

 figure: Fig. 1.

Fig. 1. Laser signals from geostationary Earth orbit travel through a large part of Earth’s gravitational potential, as well as through turbulent atmosphere. The successful characterization of quantum features under such conditions is a precondition for the implementation of a global quantum communication network using satellites. Metropolitan area quantum networks on the ground would then be provided with the currently missing links to each other. (Picture of the Earth: Google; picture of the satellite: ESA.)

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An important step for this goal is to precisely characterize the system and channel with respect to their quantum noise behavior. Coherent quantum communication encodes quantum states in the phase space and works at the limit of the Heisenberg uncertainty relation [44], but it is susceptible to additional technical noise. Our task here is to characterize whether quantum coherence properties are preserved after propagation of quantum states over 38,600 km, through a large part of gravitational potential of Earth, and through the turbulence of all atmospheric layers.

2. SPACE-TO-GROUND LINK

Our sender is a LCT flying on the GEO spacecraft Alphasat I-XL (see Fig. 2). The LCT was developed for classical coherent satellite communication (details on the LCT may be found in [4143]). It is based on an Nd:YAG laser operated at a wavelength of 1064 nm in continuous-wave mode. After passing through an amplitude modulator, a phase modulator at a frequency of 2.8 GHz imprints an alphabet of binary phase modulated coherent states |α and |α on the light field [46]. The same type of binary phase modulation can be used in quantum communication [39,47] together with quaternary phase modulation to increase performance [39,48]. Subsequently, the coherent quantum states are amplified and have thermal excess noise, defined as noise above the quantum uncertainty of the vacuum state (usually referred to as shot noise). A periscope with a diameter 13.5 cm precisely points the laser beam to the optical ground station. On the ground, we use the Transportable Adaptive Optical Ground Station (TAOGS, see Fig. 2) for pointing, acquisition, and tracking [25] of the laser beam from space. An adaptive optics system corrects for phase front distortions to launch the beam into a single mode fiber. Our quantum acquisition system uses a homodyne detector [49] (with a clearance of up to 6 dB, see Supplement 1 for details) to measure field variables in the continuous-variable (CV) regime [50,51]. The local oscillator is a tunable Nd:YAG laser that is frequency locked by a locking loop. Part of the signal is split off to lock the phase to that of an optical phase lock loop. This method enables characterization of the quadratures of the light field with a sensitivity at the quantum noise limit (details may be found in [25,42,45]).

 figure: Fig. 2.

Fig. 2. Space-to-ground link setup. A LCT on the Alphasat I-XL spacecraft in GEO links in continuous-wave (cw) mode to the TAOGS) [45], currently located at the Teide Observatory in Tenerife, Spain. The TAOGS is equipped with a quantum signal acquisition system based on the homodyne principle, where a weak quantum signal interferes with a local oscillator reference beam. By mode-matching the local oscillator to the signal, stray light is filtered out such that daylight causes no operational constraints. (Picture of Alphasat: ESA.)

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The total loss from the satellite output up to the receiving aperture was measured to be 69 dB. This value incorporates the following sources of losses: Most of the channel attenuation stems from the receiving aperture of 27 cm being smaller than the spot size at the ground station. Loss through scattering and absorption at atmospheric particles is very low under good weather conditions and assumed here to be less than 2 dB. Turbulence induced beam spread and scintillation result in a small loss of about 1 dB. Besides that, there are losses through waveform aberrations and pointing errors. Note, that beam wandering induced losses, which are important in shorter links [52], are small as the beam diameter is significantly larger than the receiving aperture. Technical losses within the TAOGS are kept at a level of 16 dB (including detector quantum efficiencies). Thus, in total the losses from the sending aperture to the detector add up to 85 dB.

3. DATA ANALYSIS AND MEASUREMENT RESULTS

We focus our measurements and data analysis on the X quadrature in which the signal is encoded [53] We sample our data points with 40 GS/s. To estimate the pulse centers, we perform a clock recovery by digital post-processing of the raw data. Details of the asynchronous sampling procedure are given in Supplement 1. The amplitude modulator in the LCT can sinusoidally vary the signal amplitudes, with slower frequency than the phase modulation. We acquire the signal states of varying amplitudes and sort them into 50 bins of quasi equal amplitude, each containing about 70,000 measurement values. This method allows us to produce histograms of X quadrature values for each bin (three of which are shown in Fig. 3).

 figure: Fig. 3.

Fig. 3. Experimental results for excess noise variance in units of quantum uncertainty of the vacuum state (shot noise unit snu). Data is shown for different detected signal amplitudes, |α| (the mean amplitude is 0.86). In the upper row, three exemplary histograms (|α|=0.63,0.92,1.24) illustrate the observed quadrature distribution along the X quadrature. Each of the histograms contains about 70,000 data points.

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A binary phase modulation of coherent states produces a double Gaussian measurement distribution in a quantum-limited homodyne detection system. As we can see in Fig. 3, our experimental data agree well with this prediction. Therefore, we can determine the amplitude and the variance of the received quantum states using a double Gaussian fit, assuming that the variances of the two states |+α and |α are equal. We normalize our measured signal states to a reference measurement of the quantum vacuum state by closing the signal port of the homodyne receiver. We verify the linearity of the photodetectors and subtract the electronic noise variance from both signal variance and vacuum variance in all measurements (see Supplement 1).

Dividing the signal variances by the vacuum variance yields the vacuum-normalized variances and allows to deduce the amplitudes of our signal states in the X quadrature (see Fig. 3). Our measured excess noise contains excess noise picked up during propagation through the atmosphere, as well as all potential technical noise in the ground station before detection. Nevertheless, we observe a signal variance of 1.01±0.03 in units of the quantum uncertainty of the vacuum state and thus conclude that the detected signal states are almost quantum uncertainty limited coherent states. This means that our result is consistent with vanishingly small excess noise within the error bars. Excess noise is an important parameter for continuous-variable QKD which can be seen as counterpart of the Quantum Bit Error Rate in discrete-variable QKD [54]. Besides excess noise, losses are important to consider for QKD applications, which will be discussed in the next paragraph. Note that both parameters are treated independently of each other.

4. FEASIBILITY OF SATELLITE QUANTUM COMMUNICATION

Our measurement results show that coherence properties can be preserved even after very long propagation and through Earth’s atmospheric layers. Using a low-noise phase-locking mechanism based on homodyne detection, quantum communication protocols using phase encoding become possible. For each protocol, the main parameter which remains to be optimized for QKD applications is the channel loss. This can mostly be done by the use of a bigger receiving aperture. The channel loss from GEO with an increased ground aperture of 1.5 m would be reduced by 14 dB from 69 dB to 55 dB. By improving the technical loss, discrete-variable QKD protocols, employing differential phase-shift keying or decoy states, operated from a GEO-stationary satellite, then become feasible [5562] (an exemplary description of a QKD protocol together with the system changes which would be necessary can be found in Supplement 1). For continuous-variable (CV) QKD protocols with coherent detection, using Gaussian modulation [63] or Gaussian post-selection [64] an operation in low Earth orbit is conceivable. Assuming an Alphasat-like LCT in a LEO orbit at a distance of 500 km the channel losses of 69 dB would be reduced to 31 dB. Using a bigger receiving aperture of 1 m could reduce the losses by another 11 dB. Thus, the channel loss from a LEO satellite is estimated to be around 20 dB, what is within the tolerable amount of loss given in [64], even adding the typical amount of technical loss.

These considerations may be extended to quadrature phase-shift keying (QPSK), bearing in mind that security proofs for CV discrete-modulation protocols still need to improve to support quantum channels with higher losses. Note, that future laser communication terminals for quantum communication require adjusted sending amplitudes and reduced internal excess noise by suitably multiplexing classical and quantum mode. Additionally, also the ground station should be optimized for QKD applications, for example in terms of technical losses and detector clearance.

5. BOUND ON EXCESS NOISE

An interesting aspect is that our measurement data allows us to study the influence of the atmosphere on the propagation of quantum states. Initially, the states are prepared by the LCT with an excess noise of 33 dB above the quantum uncertainty of the vacuum state. We assume that the propagation through the almost particle-free exosphere only has negligible influence on the quantum states. Imagine a virtual receiver with a receiving aperture of the size of the TAOGS aperture at an altitude of 1000 km above ground. This virtual aperture would observe an intensity reduced by a factor of 61 dB, governed by the geometrical beam expansion (see Fig. 4). Due to the same loss, excess noise would be reduced to merely 0.001 units above the quantum uncertainty of the vacuum state. Both excess noise picked up during propagation through the atmosphere and technical excess noise originating at the receiver on ground is visible in our measurement data. However, both the atmosphere and our receiver are not loss-free, which implies that higher excess noise than actually measured might have been present during propagation. To give a worst case bound for this value, we scale the measured excess noise up, from a value of 0.01±0.03 by a factor of 16 dB (ground station losses) resulting in 0.4±1.2. Additionally, we scale this value with atmospheric losses of 3 dB and obtain an upper bound for the excess noise of 0.8±2.4 (see Supplement 1). Note that this is a conservative estimate for both the atmospheric and technical excess noise. Whereas excess noise originating during propagation has to be scaled up this is not the case for noise originating at the receiver on ground, lowering the bound significantly. According to our estimation both noise sources cannot be distinguished. The estimated bound only relies on the linear loss assumption and not on any specific noise model which makes it a very general result.

 figure: Fig. 4.

Fig. 4. Satellite in geostationary Earth orbit produces two phase-encoded thermal states. Due to the high channel attenuation, the thermal states converge to coherent quantum states on their way down to Earth. Therefore, a receiver at an altitude of 1000 km above ground would detect nearly quantum uncertainty limited signals. At the same position, we can image a virtual aperture transmitting quantum uncertainty limited states. Using this model, we can estimate an upper bound for atmospheric influence of 0.8±2.4 above the quantum uncertainty of the vacuum state (see Supplement 1). (Picture of the satellite: ESA.)

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Using the same estimate, our quantum-limited measurements on ground bound the excess noise that could have been added during the whole propagation through the Earth’s gravitational potential. Taking into account the overall loss of 85 dB between satellite and detector on ground, we can give a first bound of any excess noise being below 65 dB, well in agreement with the 33 dB of thermal excess noise originating from the satellite (see section on amplifier noise behavior in Supplement 1).

6. CONCLUSION AND OUTLOOK

Concerning the implementation of satellite QKD, we have presented phase space measurements of optical signals sent from geostationary Earth orbit (GEO) to an optical ground station. We have shown by measurement that quantum limited states arrive at the ground station despite the long propagation path including Earth’s atmospheric layers. We have bound the overall excess noise that can degrade the quantum states in the satellite-ground link and the atmospheric layers. This work can be seen as the first step in developing quantum communication from GEO. While the currently existing hardware is optimized for classical coherent data communication, the technological proximity to coherent quantum communication opens up a fast and efficient way to develop a global quantum network. Moreover, beyond the strict QKD regime our results can be adopted to the overall context of security by physical means (see e.g., [65]) as a powerful line of defense against future cyber-attacks [66].

Acknowledgment

The LCT and TAOGS are supported by the German Aerospace Center (DLR) Space Administration, with funds from the Federal Ministry for Economic Affairs and Energy according to a decision of the German Federal Parliament.

We thank Bettina Heim, Christian Peuntinger, Nathan Killoran, Kaushik Seshadreesan, Radim Filip, Norbert Lütkenhaus, Christoph Pacher, Zoran Sodnik and Harald Hauschildt for fruitful discussions. We furthermore thank the European Space Agency (ESA) for hosting TAOGS next to the ESA Optical Ground Station (OGS) in Tenerife.

 

See Supplement 1 for supporting content.

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64. N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian post selection,” Phys. Rev. A 87, 020303 (2013). [CrossRef]  

65. M. M. Wilde, Quantum Information Theory (Cambridge University, 2013).

66. H. Endo, M. Fujiwara, M. Kitamura, T. Ito, M. Toyoshima, Y. Takayama, H. Takenaka, R. Shimizu, N. Laurenti, G. Vallone, P. Villoresi, T. Aoki, and M. Sasaki, “Free-space optical channel estimation for physical layer security,” Opt. Express 24, 8940–8955 (2016). [CrossRef]  

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  53. For continuous-variable QKD, the P quadrature needs to be measured simultaneously, which will be a subject of future studies.
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  61. B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photonics 9, 163–168 (2015).
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    [Crossref]
  63. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
    [Crossref]
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    [Crossref]

2016 (8)

M. T. Gruneisen, B. A. Sickmiller, M. B. Flanagan, J. P. Black, K. E. Stoltenberg, and A. W. Duchane, “Adaptive spatial filtering of daytime sky noise in a satellite quantum key distribution downlink receiver,” Opt. Eng. 55, 026104 (2016).
[Crossref]

Z. Tang, R. Chandrasekara, Y. C. Tan, C. Cheng, L. Sha, G. C. Hiang, D. K. L. Oi, and A. Ling, “Generation and analysis of correlated pairs of photons aboard a nanosatellite,” Phys. Rev. Appl. 5, 054022 (2016).
[Crossref]

D. Dequal, G. Vallone, D. Bacco, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental single-photon exchange along a space link of 7000 km,” Phys. Rev. A 93, 010301 (2016).
[Crossref]

A. Carrasco-Casado, H. Kunimori, H. Takenaka, T. Kubo-Oka, M. Akioka, T. Fuse, Y. Koyama, D. Kolev, Y. Munemasa, and M. Toyoshima, “LEO-to-ground polarization measurements aiming for space QKD using small optical transponder (SOTA),” Opt. Express 24, 12254–12266 (2016).
[Crossref]

E. Gibney, “Chinese satellite is one giant step for the quantum internet,” Nature 535, 478–479 (2016).
[Crossref]

K. Saucke, C. Seiter, F. Heine, M. Gregory, D. Tröndle, E. Fischer, T. Berkefeld, M. Feriencik, M. Feriencik, I. Richter, and R. Meyer, “The Tesat transportable adaptive optical ground station,” Proc. SPIE 9739, 973906 (2016).
[Crossref]

D. Vasylyev, A. A. Semenov, and W. Vogel, “Atmospheric quantum channels with weak and strong turbulence,” Phys. Rev. Lett. 117, 090501 (2016).
[Crossref]

H. Endo, M. Fujiwara, M. Kitamura, T. Ito, M. Toyoshima, Y. Takayama, H. Takenaka, R. Shimizu, N. Laurenti, G. Vallone, P. Villoresi, T. Aoki, and M. Sasaki, “Free-space optical channel estimation for physical layer security,” Opt. Express 24, 8940–8955 (2016).
[Crossref]

2015 (5)

B. Korzh, C. C. W. Lim, R. Houlmann, N. Gisin, M. J. Li, D. Nolan, B. Sanguinetti, R. Thew, and H. Zbinden, “Provably secure and practical quantum key distribution over 307 km of optical fibre,” Nat. Photonics 9, 163–168 (2015).
[Crossref]

J.-P. Bourgoin, N. Gigov, B. L. Higgins, Z. Yan, E. Meyer-Scott, A. K. Khandani, N. Lütkenhaus, and T. Jennewein, “Experimental quantum key distribution with simulated ground-to-satellite photon losses and processing limitations,” Phys. Rev. A 92, 052339 (2015).
[Crossref]

F. Heine, G. Mühlnikel, H. Zech, D. Tröndle, S. Seel, M. Motzigemba, R. Meyer, S. Philipp-May, and E. Benzi, “LCT for the European data relay system: in orbit commissioning of the Alphasat and Sentinel 1A LCTs,” Proc. SPIE 9354, 93540G (2015).
[Crossref]

H. Zech, F. Heine, D. Tröndle, S. Seel, M. Motzigemba, R. Meyer, and S. Philipp-May, “LCT for EDRS: LEO to GEO optical communications at 1, 8 Gbps between Alphasat and Sentinel 1a,” Proc. SPIE 9647, 96470J (2015).
[Crossref]

A. Aspect, “Viewpoint: closing the door on Einstein and Bohr’s quantum debate,” Physics 8, 123 (2015).
[Crossref]

2014 (7)

T. C. Ralph and J. Pienaar, “Entanglement decoherence in a gravitational well according to the event formalism,” New J. Phys. 16, 085008 (2014).
[Crossref]

D. E. Bruschi, T. C. Ralph, I. Fuentes, T. Jennewein, and M. Razavi, “Spacetime effects on satellite-based quantum communications,” Phys. Rev. D 90, 045041 (2014).
[Crossref]

C. Peuntinger, B. Heim, C. R. Müller, C. Gabriel, C. Marquardt, and G. Leuchs, “Distribution of squeezed states through an atmospheric channel,” Phys. Rev. Lett. 113, 060502 (2014).
[Crossref]

B. Heim, C. Peuntinger, N. Killoran, I. Khan, C. Wittmann, C. Marquardt, and G. Leuchs, “Atmospheric continuous-variable quantum communication,” New J. Phys. 16, 113018 (2014).
[Crossref]

D. M. Boroson, B. S. Robinson, D. V. Murphy, D. A. Burianek, F. Khatri, J. M. Kovalik, Z. Sodnik, and D. M. Cornwell, “Overview and results of the lunar laser communication demonstration,” Proc. SPIE 8971, 89710S (2014).
[Crossref]

J.-W. Pan, “Quantum science satellite,” Chin. J. Space Sci. 34, 547–549 (2014).

H. Shibata, T. Honjo, and K. Shimizu, “Quantum key distribution over a 72 dB channel loss using ultralow dark count superconducting single-photon detectors,” Opt. Lett. 39, 5078–5081 (2014).
[Crossref]

2013 (5)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

N. Walk, T. C. Ralph, T. Symul, and P. K. Lam, “Security of continuous-variable quantum cryptography with Gaussian post selection,” Phys. Rev. A 87, 020303 (2013).
[Crossref]

T. Scheidl, E. Wille, and R. Ursin, “Quantum optics experiments using the International Space Station: a proposal,” New J. Phys. 15, 043008 (2013).
[Crossref]

T. Jennewein and B. Higgins, “The quantum space race,” Phys. World 26, 52–56 (2013).
[Crossref]

L. Bacsardi, “On the way to quantum-based satellite communication,” IEEE Commun. Mag. 51(8), 50–55 (2013).
[Crossref]

2012 (3)

Z. Merali, “Data teleportation: the quantum space race,” Nature 492, 22–25 (2012).
[Crossref]

D. Rideout, T. Jennewein, G. Amelino-Camelia, T. F. Demarie, B. L. Higgins, A. Kempf, A. Kent, R. Laflamme, X. Ma, R. B. Mann, E. Martn-Martnez, N. C. Menicucci, J. Moffat, C. Simon, R. Sorkin, L. Smolin, and D. R. Terno, “Fundamental quantum optics experiments conceivable with satellites––reaching relativistic distances and velocities,” Classical Quantum Gravity 29, 224011 (2012).
[Crossref]

N. Killoran, M. Hosseini, B. C. Buchler, P. K. Lam, and N. Lütkenhaus, “Quantum benchmarking with realistic states of light,” Phys. Rev. A 86, 022331 (2012).
[Crossref]

2009 (4)

D. Elser, T. Bartley, B. Heim, C. Wittmann, D. Sych, and G. Leuchs, “Feasibility of free space quantum key distribution with coherent polarization states,” New J. Phys. 11, 045014 (2009).
[Crossref]

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gbps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
[Crossref]

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
[Crossref]

2007 (2)

T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, “Experimental demonstration of free-space decoy-state quantum key distribution over 144 km,” Phys. Rev. Lett. 98, 010504 (2007).
[Crossref]

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Furst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481–486 (2007).
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2006 (2)

S. Lorenz, J. Rigas, M. Heid, U. L. Andersen, N. Lütkenhaus, and G. Leuchs, “Witnessing effective entanglement in a continuous variable prepare-and-measure setup and application to a quantum key distribution scheme using post selection,” Phys. Rev. A 74, 042326 (2006).
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R. Plaga, “A fundamental threat to quantum cryptography: gravitational attacks,” Eur. Phys. J. D 38, 409–413 (2006).
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2005 (3)

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94, 230503 (2005).
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X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
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H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
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2004 (1)

S. Lorenz, N. Korolkova, and G. Leuchs, “Continuous-variable quantum key distribution using polarization encoding and post selection,” Appl. Phys. B 79, 273–277 (2004).
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2003 (1)

W.-Y. Hwang, “Quantum key distribution with high loss: toward global secure communication,” Phys. Rev. Lett. 91, 057901 (2003).
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2002 (4)

K. Inoue, E. Waks, and Y. Yamamoto, “Differential phase shift quantum key distribution,” Phys. Rev. Lett. 89, 037902 (2002).
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C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901 (2002).
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R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43 (2002).
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J. G. Rarity, P. R. Tapster, P. M. Gorman, and P. Knight, “Ground to satellite secure key exchange using quantum cryptography,” New J. Phys. 4, 82 (2002).
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2000 (2)

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515–519 (2000).
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W. T. Buttler, R. J. Hughes, S. K. Lamoreaux, G. L. Morgan, J. E. Nordholt, and C. G. Peterson, “Daylight quantum key distribution over 1.6 km,” Phys. Rev. Lett. 84, 5652–5655 (2000).
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1999 (1)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303 (1999).
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1998 (1)

W. T. Buttler, R. J. Hughes, P. G. Kwiat, G. G. Luther, G. L. Morgan, J. E. Nordholt, C. G. Peterson, and C. M. Simmons, “Free-space quantum-key distribution,” Phys. Rev. A 57, 2379–2382 (1998).
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1995 (1)

Y. Arimoto, M. Toyoshima, M. Toyoda, T. Takahashi, M. Shikatani, and K. Araki, “Preliminary result on laser communication experiment using (ETS-VI),” Proc. SPIE 2381, 151 (1995).
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1992 (1)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
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1963 (1)

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
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1927 (1)

W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Z. Phys. 43, 172–198 (1927).
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Acin, A.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Akioka, M.

A. Carrasco-Casado, H. Kunimori, H. Takenaka, T. Kubo-Oka, M. Akioka, T. Fuse, Y. Koyama, D. Kolev, Y. Munemasa, and M. Toyoshima, “LEO-to-ground polarization measurements aiming for space QKD using small optical transponder (SOTA),” Opt. Express 24, 12254–12266 (2016).
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M. Toyoshima, T. Fuse, D. R. Kolev, H. Takenaka, Y. Munemasa, N. Iwakiri, K. Suzuki, Y. Koyama, T. Kubooka, M. Akioka, and H. Kunimori, “Current status of research and development on space laser communications technologies and future plans in NICT,” in International Conference on Space Optical Systems and Applications (ICSOS) (IEEE, 2015).

Amelino-Camelia, G.

D. Rideout, T. Jennewein, G. Amelino-Camelia, T. F. Demarie, B. L. Higgins, A. Kempf, A. Kent, R. Laflamme, X. Ma, R. B. Mann, E. Martn-Martnez, N. C. Menicucci, J. Moffat, C. Simon, R. Sorkin, L. Smolin, and D. R. Terno, “Fundamental quantum optics experiments conceivable with satellites––reaching relativistic distances and velocities,” Classical Quantum Gravity 29, 224011 (2012).
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Andersen, U. L.

S. Lorenz, J. Rigas, M. Heid, U. L. Andersen, N. Lütkenhaus, and G. Leuchs, “Witnessing effective entanglement in a continuous variable prepare-and-measure setup and application to a quantum key distribution scheme using post selection,” Phys. Rev. A 74, 042326 (2006).
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Aoki, T.

Araki, K.

Y. Arimoto, M. Toyoshima, M. Toyoda, T. Takahashi, M. Shikatani, and K. Araki, “Preliminary result on laser communication experiment using (ETS-VI),” Proc. SPIE 2381, 151 (1995).
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Arimoto, Y.

Y. Arimoto, M. Toyoshima, M. Toyoda, T. Takahashi, M. Shikatani, and K. Araki, “Preliminary result on laser communication experiment using (ETS-VI),” Proc. SPIE 2381, 151 (1995).
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Aspect, A.

A. Aspect, “Viewpoint: closing the door on Einstein and Bohr’s quantum debate,” Physics 8, 123 (2015).
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R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Bacco, D.

D. Dequal, G. Vallone, D. Bacco, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental single-photon exchange along a space link of 7000 km,” Phys. Rev. A 93, 010301 (2016).
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Bacsardi, L.

L. Bacsardi, “On the way to quantum-based satellite communication,” IEEE Commun. Mag. 51(8), 50–55 (2013).
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Barbieri, C.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Furst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481–486 (2007).
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Bartley, T.

D. Elser, T. Bartley, B. Heim, C. Wittmann, D. Sych, and G. Leuchs, “Feasibility of free space quantum key distribution with coherent polarization states,” New J. Phys. 11, 045014 (2009).
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Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
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Bennett, C. H.

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
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Benzi, E.

F. Heine, G. Mühlnikel, H. Zech, D. Tröndle, S. Seel, M. Motzigemba, R. Meyer, S. Philipp-May, and E. Benzi, “LCT for the European data relay system: in orbit commissioning of the Alphasat and Sentinel 1A LCTs,” Proc. SPIE 9354, 93540G (2015).
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Berkefeld, T.

K. Saucke, C. Seiter, F. Heine, M. Gregory, D. Tröndle, E. Fischer, T. Berkefeld, M. Feriencik, M. Feriencik, I. Richter, and R. Meyer, “The Tesat transportable adaptive optical ground station,” Proc. SPIE 9739, 973906 (2016).
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E. Fischer, T. Berkefeld, M. Feriencik, M. Feriencik, V. Kaltenbach, D. Soltau, B. Wandernoth, R. Czichy, and J. Kunde, “Development, integration and test of a transportable adaptive optical ground station,” in International Conference on Space Optical Systems and Applications (ICSOS) (IEEE, 2015).

Bernstein, H.

T. Graham, C. Zeitler, J. Chapman, P. Kwiat, H. Javadi, and H. Bernstein, “Superdense teleportation and quantum key distribution for space applications,” in International Conference on Space Optical Systems and Applications (ICSOS) (IEEE, 2015).

Bianco, G.

D. Dequal, G. Vallone, D. Bacco, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental single-photon exchange along a space link of 7000 km,” Phys. Rev. A 93, 010301 (2016).
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R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Biever, C.

C. Biever, “China’s quantum space pioneer: we need to explore the unknown,” Nature (2016), 10.1038/nature.2016.19166.
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Black, J. P.

M. T. Gruneisen, B. A. Sickmiller, M. B. Flanagan, J. P. Black, K. E. Stoltenberg, and A. W. Duchane, “Adaptive spatial filtering of daytime sky noise in a satellite quantum key distribution downlink receiver,” Opt. Eng. 55, 026104 (2016).
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Blauensteiner, B.

R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Omer, M. Furst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481–486 (2007).
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Boehmer, K.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gbps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
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Boroson, D. M.

D. M. Boroson, B. S. Robinson, D. V. Murphy, D. A. Burianek, F. Khatri, J. M. Kovalik, Z. Sodnik, and D. M. Cornwell, “Overview and results of the lunar laser communication demonstration,” Proc. SPIE 8971, 89710S (2014).
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Bourgoin, J.-P.

J.-P. Bourgoin, N. Gigov, B. L. Higgins, Z. Yan, E. Meyer-Scott, A. K. Khandani, N. Lütkenhaus, and T. Jennewein, “Experimental quantum key distribution with simulated ground-to-satellite photon losses and processing limitations,” Phys. Rev. A 92, 052339 (2015).
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Bouwmeester, D.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515–519 (2000).
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Brukner, C.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Bruschi, D. E.

D. E. Bruschi, T. C. Ralph, I. Fuentes, T. Jennewein, and M. Razavi, “Spacetime effects on satellite-based quantum communications,” Phys. Rev. D 90, 045041 (2014).
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Buchler, B. C.

N. Killoran, M. Hosseini, B. C. Buchler, P. K. Lam, and N. Lütkenhaus, “Quantum benchmarking with realistic states of light,” Phys. Rev. A 86, 022331 (2012).
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Burianek, D. A.

D. M. Boroson, B. S. Robinson, D. V. Murphy, D. A. Burianek, F. Khatri, J. M. Kovalik, Z. Sodnik, and D. M. Cornwell, “Overview and results of the lunar laser communication demonstration,” Proc. SPIE 8971, 89710S (2014).
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Buttler, W. T.

W. T. Buttler, R. J. Hughes, S. K. Lamoreaux, G. L. Morgan, J. E. Nordholt, and C. G. Peterson, “Daylight quantum key distribution over 1.6 km,” Phys. Rev. Lett. 84, 5652–5655 (2000).
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W. T. Buttler, R. J. Hughes, P. G. Kwiat, G. G. Luther, G. L. Morgan, J. E. Nordholt, C. G. Peterson, and C. M. Simmons, “Free-space quantum-key distribution,” Phys. Rev. A 57, 2379–2382 (1998).
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R. J. Hughes, W. T. Buttler, P. G. Kwiat, S. K. Lamoreuax, G. L. Morgan, J. E. Nordholt, and C. G. Peterson, “Quantum cryptography for secure satellite communications,” in IEEE Aerospace Conference Proceedings (2000), Vol. 1, pp. 191–200.

Cacciapuoti, L.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Campo, R.

D. Elser, S. Seel, F. Heine, T. Länger, M. Peev, D. Finocchiaro, R. Campo, A. Rechhia, A. Le Pera, T. Scheidl, R. Ursin, and Z. Sodnik, “Network architectures for space-optical quantum cryptography services,” in International Conference on Space Optical Systems and Applications (ICSOS) (IEEE, 2012).

Capmany, J.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Carrasco-Casado, A.

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81, 1301–1350 (2009).
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Chandrasekara, R.

Z. Tang, R. Chandrasekara, Y. C. Tan, C. Cheng, L. Sha, G. C. Hiang, D. K. L. Oi, and A. Ling, “Generation and analysis of correlated pairs of photons aboard a nanosatellite,” Phys. Rev. Appl. 5, 054022 (2016).
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Chapman, J.

T. Graham, C. Zeitler, J. Chapman, P. Kwiat, H. Javadi, and H. Bernstein, “Superdense teleportation and quantum key distribution for space applications,” in International Conference on Space Optical Systems and Applications (ICSOS) (IEEE, 2015).

Chen, K.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
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Cheng, C.

Z. Tang, R. Chandrasekara, Y. C. Tan, C. Cheng, L. Sha, G. C. Hiang, D. K. L. Oi, and A. Ling, “Generation and analysis of correlated pairs of photons aboard a nanosatellite,” Phys. Rev. Appl. 5, 054022 (2016).
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Cornwell, D. M.

D. M. Boroson, B. S. Robinson, D. V. Murphy, D. A. Burianek, F. Khatri, J. M. Kovalik, Z. Sodnik, and D. M. Cornwell, “Overview and results of the lunar laser communication demonstration,” Proc. SPIE 8971, 89710S (2014).
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Cova, S.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Czichy, R.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gbps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
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E. Fischer, T. Berkefeld, M. Feriencik, M. Feriencik, V. Kaltenbach, D. Soltau, B. Wandernoth, R. Czichy, and J. Kunde, “Development, integration and test of a transportable adaptive optical ground station,” in International Conference on Space Optical Systems and Applications (ICSOS) (IEEE, 2015).

Dallmann, D.

B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gbps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
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Daniell, M.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515–519 (2000).
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de Matos, C. J.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Demarie, T. F.

D. Rideout, T. Jennewein, G. Amelino-Camelia, T. F. Demarie, B. L. Higgins, A. Kempf, A. Kent, R. Laflamme, X. Ma, R. B. Mann, E. Martn-Martnez, N. C. Menicucci, J. Moffat, C. Simon, R. Sorkin, L. Smolin, and D. R. Terno, “Fundamental quantum optics experiments conceivable with satellites––reaching relativistic distances and velocities,” Classical Quantum Gravity 29, 224011 (2012).
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Dequal, D.

D. Dequal, G. Vallone, D. Bacco, S. Gaiarin, V. Luceri, G. Bianco, and P. Villoresi, “Experimental single-photon exchange along a space link of 7000 km,” Phys. Rev. A 93, 010301 (2016).
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Derkacs, D.

R. J. Hughes, J. E. Nordholt, D. Derkacs, and C. G. Peterson, “Practical free-space quantum key distribution over 10 km in daylight and at night,” New J. Phys. 4, 43 (2002).
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Diamanti, E.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
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B. Smutny, H. Kaempfner, G. Muehlnikel, U. Sterr, B. Wandernoth, F. Heine, U. Hildebrand, D. Dallmann, M. Reinhardt, A. Freier, R. Lange, K. Boehmer, T. Feldhaus, J. Mueller, A. Weichert, P. Greulich, S. Seel, R. Meyer, and R. Czichy, “5.6 Gbps optical intersatellite communication link,” Proc. SPIE 7199, 719906 (2009).
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K. Saucke, C. Seiter, F. Heine, M. Gregory, D. Tröndle, E. Fischer, T. Berkefeld, M. Feriencik, M. Feriencik, I. Richter, and R. Meyer, “The Tesat transportable adaptive optical ground station,” Proc. SPIE 9739, 973906 (2016).
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Valencia, A.

R. Ursin, T. Jennewein, J. Kofler, J. M. Perdigues, L. Cacciapuoti, C. J. de Matos, M. Aspelmeyer, A. Valencia, T. Scheidl, A. Acin, C. Barbieri, G. Bianco, C. Brukner, J. Capmany, S. Cova, D. Giggenbach, W. Leeb, R. H. Hadfield, R. Laflamme, N. Lütkenhaus, G. Milburn, M. Peev, T. Ralph, J. Rarity, R. Renner, E. Samain, N. Solomos, W. Tittel, J. P. Torres, M. Toyoshima, A. Ortigosa-Blanch, V. Pruneri, P. Villoresi, I. Walmsley, G. Weihs, H. Weinfurter, M. Zukowski, and A. Zeilinger, “Space-quest, experiments with quantum entanglement in space,” Europhys. News 40, 26–29 (2009).
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Supplementary Material (1)

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Supplement 1: PDF (1564 KB)      Supplementary Material

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Figures (4)

Fig. 1.
Fig. 1. Laser signals from geostationary Earth orbit travel through a large part of Earth’s gravitational potential, as well as through turbulent atmosphere. The successful characterization of quantum features under such conditions is a precondition for the implementation of a global quantum communication network using satellites. Metropolitan area quantum networks on the ground would then be provided with the currently missing links to each other. (Picture of the Earth: Google; picture of the satellite: ESA.)
Fig. 2.
Fig. 2. Space-to-ground link setup. A LCT on the Alphasat I-XL spacecraft in GEO links in continuous-wave (cw) mode to the TAOGS) [45], currently located at the Teide Observatory in Tenerife, Spain. The TAOGS is equipped with a quantum signal acquisition system based on the homodyne principle, where a weak quantum signal interferes with a local oscillator reference beam. By mode-matching the local oscillator to the signal, stray light is filtered out such that daylight causes no operational constraints. (Picture of Alphasat: ESA.)
Fig. 3.
Fig. 3. Experimental results for excess noise variance in units of quantum uncertainty of the vacuum state (shot noise unit snu). Data is shown for different detected signal amplitudes, | α | (the mean amplitude is 0.86). In the upper row, three exemplary histograms ( | α | = 0.63 , 0.92 , 1.24 ) illustrate the observed quadrature distribution along the X quadrature. Each of the histograms contains about 70,000 data points.
Fig. 4.
Fig. 4. Satellite in geostationary Earth orbit produces two phase-encoded thermal states. Due to the high channel attenuation, the thermal states converge to coherent quantum states on their way down to Earth. Therefore, a receiver at an altitude of 1000 km above ground would detect nearly quantum uncertainty limited signals. At the same position, we can image a virtual aperture transmitting quantum uncertainty limited states. Using this model, we can estimate an upper bound for atmospheric influence of 0.8 ± 2.4 above the quantum uncertainty of the vacuum state (see Supplement 1). (Picture of the satellite: ESA.)

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