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 of Gaussian states and the applicability to quantum key distribution over fading channels T h e o p e n -a c c e s s j o u r n a l f o r p h y s i c s New Journal of PhysicsEntanglement of Gaussian states and the applicability to quantum key distribution over fading channels Abstract. Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication.We introduce a method of fading discrimination and subsequent post-selection of the corresponding sub-states and show that it can improve the entanglement 6 Authors to whom any correspondence should be addressed.Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercialShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 14 (2012) 0930481367-2630/12/093048+20$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 resource and restore the security of the key distribution over a realistic fading link. Furthermore, the optimal post-selection strategy in combination with an optimized entangled resource is shown to drastically increase the protocol's robustness to excess noise, which is confirmed for experimentally measured fading channel characteristics. The stability of the result against finite data ensemble size and imperfect channel estimation is also addressed. Contents
Continuous variable quantum states of light are used in quantum information protocols and quantum metrology and known to degrade with loss and added noise. We were able to show the distribution of bright polarization squeezed quantum states of light through an urban free-space channel of 1.6 km length. To measure the squeezed states in this extreme environment, we utilize polarization encoding and a postselection protocol that is taking into account classical side information stemming from the distribution of transmission values. The successful distribution of continuous variable squeezed states is accentuated by a quantum state tomography, allowing for determining the purity of the state.
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