Quantum key distribution (QKD) promises informationtheoretically secure communication, and is already on the verge of commercialization. Thus far, different QKD protocols have been proposed theoretically and implemented experimentally [1, 2]. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate [3][4][5][6][7]. Hitherto, no experimental verification of high-dimensional QKD in the single-photon regime has been conducted outside of the laboratory. Here, we report the realization of such a single-photon QKD system in a turbulent free-space link of 0.3 km over the city of Ottawa, taking advantage of both the spin and orbital angular momentum photonic degrees of freedom. This combination of optical angular momenta allows us to create a 4-dimensional state [8]; wherein, using a high-dimensional BB84 protocol [3, 4], a quantum bit error rate of 11% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. While an error rate of 5% with a secret key rate of 0.43 bits per sifted photon is achieved for the case of 2-dimensional structured photons. Even through moderate turbulence without active wavefront correction, it is possible to securely transmit information carried by structured photons, opening the way for intra-city high-dimensional quantum communications under realistic conditions.In addition to wavelength and polarization, a light wave is characterized by its orbital angular momentum (OAM) [9], which corresponds to its helical wavefronts. Polarization is naturally bi-dimensional, i.e. {|L , |R }, and the associated angular momentum can take the values of ± per photon, where is the reduced Planck constant, and |L and |R are left-and right-handed circular polarizations, respectively. In contrast, OAM is inherently unbounded, such that a photon with intertwined helical wavefronts, | , carries units of OAM, where is an integer [10]. Quantum states of light resulting from an arbitrary coherent superposition of different polarizations and spatial modes, e.g. OAM, are referred to as structured photons; these photons can be used to realize higher-dimensional states of light [8]. Aside from their fundamental significance in quantum physics [11,12], single photons encoded in higher dimensions provide an advantage in terms of security tolerance and encrypting alphabets for quantum cryptography [3, 4,7] and classical communications [13]. The behaviour of light carrying OAM through turbulent conditions has been studied theoretically and simulated in the laboratory scale [14][15][16][17]. Experimentally, OAM states have been tested in classical communications across intra-city links in Los Angeles (120 m) [18], Venice (420 m) [19], Erlangen (1.6 km) [20], Vienna (3 km) [21], and between two Canary Islands (143 km) [22] which is the longest link thus far. With attenuated lasers, OAM states and vector vortex beams have been respectively implemented in high-dimensional and 2-dimensional BB84 protocols, where the former was performed ...

The measurement of quantum signals that traveled through long distances is of fundamental and technological interest. We present quantum-limited coherent measurements of optical signals, 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.Quantum mechanics has successfully undergone a number of fundamental experimental tests since its development [1][2][3]. Still some aspects pose both a theoretical and an experimental challenge, such as the relation of quantum mechanics and gravity [4][5][6]. 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 [8][9][10][11][12][13][14][15] 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 [16][17][18][19][20][21][22].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 evaluating its impact on quantum communication.Optical [27]). In parallel, free space quantum communication has made its steps out of laboratories into real-world scenarios [28][29][30][31]. It has turned out that detecting field quadratures (continuous variables) is well suited to combat disturbances from atmospheric turbulence and stray light [32][33][34]. Using these methods, the first implementation of an intra-urban free space quantum link using quantum coherent detection has been reported [35,36]. The advantage of stray light immunity applies as well to classical coherent satellite communication [37]. The similarity between these classical and quantum technologies allows us to make use of the platform of a technologically mature Laser Communication Terminal (LCT) [38][39][40] for future quantum communication (see Fig 1).An important step on this way is to precisely characterize system and channel with respect to their quantum noise behavior. Coherent quantum communication employs encoding of quantum states in phase space and works at the limit of the Heisenberg uncertainty relation [41], but 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 graviarXiv:1608.03511v2 [quant-...

Free-space optical communication links are promising channels for establishing secure quantum communication. Here we study the transmission of nonclassical light through a turbulent atmospheric link under diverse weather conditions, including rain or haze. To include these effects, the theory of light transmission through atmospheric links in the elliptic-beam approximation presented by Vasylyev et al. [D. Vasylyev et al., Phys. Rev. Lett. 117, 090501 (2016); arXiv:1604.01373] is further generalized. It is demonstrated, with good agreement between theory and experiment, that low-intensity rain merely contributes additional deterministic losses, whereas haze also introduces additional beam deformations of the transmitted light. Based on these results, we study theoretically the transmission of quadrature squeezing and Gaussian entanglement under these weather conditions.

This study of structured light’s propagation across a 1.6-km free-space link indicates that adaptations to models may be required.