High-dimensional intracity quantum cryptography with structured photons

Abstract

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 ...

Entanglement protection of high-dimensional states by adaptive optics

“…To the best of our knowledge, the evolution of entangled qutrits has only been studied theoretically [18] and in one laboratory simulation [19]. Concerning higher-dimensional systems, the only known results are a free-space QKD experiment with four-dimensional quantum states (realized via the hybridization of the helical wavefront and of the polarization of the photon), where an increased data rate with respect to two-dimensional encoding was demonstrated over a distance of 300m [20], and QKD across a 3 m channel in a turbulent underwater environment [21]. To achieve longer propagation distances, compensation schemes for turbulence-induced errors, for example with methods of adaptive optics (AO), are needed.…”

Large-alphabet quantum key distribution using spatially encoded light

“…Several methods of high-dimensional QKD have been demonstrated, including time-bin [19][20][21][22], orbital angular-momentum [23][24][25][26] and transverse momentum [27,28]. Comparing the last two spatial encoding schemes, transverse momentum states have the following advantages.…”

Phenomenology of complex structured light in turbulent air

“…Since 2014, the first outdoor experiments with spatial modes were conducted, with long-distance transmissions up to 143 km [32,33], with high-speed data rates up to 400Gbit/sec [34,35], and in the quantum regime with entangled photons [33] and for quantum communication [36]. These results establish the feasibility of long-distance transmission of spatial modes of light but left open the question about the predictive power of current models.…”