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 ...

Quantum annealers use quantum fluctuations to escape local minima and find low-energy configurations of a physical system. Strong evidence for superiority of quantum annealing (QA) has come from comparing QA implemented through quantum Monte Carlo (QMC) simulations to classical annealing. Motivated by recent experiments, we revisit the question of when quantum speedup may be expected. Although a better scaling is seen for QA in two-dimensional Ising spin glasses, this advantage is due to time discretization artifacts and measurements that are not possible on a physical quantum annealer. Simulations in the physically relevant continuous time limit, on the other hand, do not show superiority. Our results imply that care must be taken when using QMC simulations to assess the potential for quantum speedup.

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

We demonstrate for the first time the feasibility of free space quantum key distribution with continuous variables under real atmospheric conditions. More specifically, we transmit coherent polarization states over a 100 m free space channel on the roof of our institute's building. In our scheme, signal and local oscillator are combined in a single spatial mode which autocompensates atmospheric fluctuations and results in an excellent interference. Furthermore, the local oscillator acts as spatial and spectral filter thus allowing unrestrained daylight operation.

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.

We present a detailed circuit implementation of Szegedy's quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly arithmetic operations. We thus reformulate the quantum walk, circumventing its implementation altogether by closely following the classical Metropolis-Hastings walk. We also present heuristic quantum algorithms that use the quantum walk in the context of discrete optimization problems and numerically study their performances. Our numerical results indicate polynomial quantum speedups in heuristic settings.

We present a quantum communication experiment conducted over a point-topoint free-space link of 1.6 km in urban conditions. We study atmospheric influences on the capability of the link to act as a continuous-variable (CV) quantum channel. Continuous polarization states (that contain the signal encoding as well as a local oscillator (LO) in the same spatial mode) are prepared and sent over the link in a polarization multiplexed setting. Both signal and LO undergo the same atmospheric fluctuations. These are intrinsically autocompensated which removes detrimental influences on the interferometric visibility. At the receiver, we measure the Q-function and interpret the data using the framework of effective entanglement (EE). We compare different state amplitudes and alphabets (two-state and four-state) and determine their optimal working points with respect to the distributed EE. Based on the high entanglement transmission rates achieved, our system indicates the high potential of atmospheric links in the field of CV quantum key distribution. 6 Contributed equally to this work.Quantum communication refers to the distribution of quantum states between two parties via a quantum channel. With regard to this, it is crucial that this quantum channel preserves the quantum properties of the distributed states. The most common channel implementations are optical fibers and free space. The latter offers great flexibility in terms of infrastructure establishment and links to moving objects are also feasible, see e.g. [1]. For a review of representative free-space quantum communication experiments see [2].Quantum key distribution (QKD) [3,4] is probably the most practical branch of quantum communication and concerns the establishment of a secret key jointly between two legitimate parties, Alice and Bob. As the security is based on the laws of quantum mechanics, in principle information theoretic-security can be achieved [4].Free-space QKD over a real atmospheric channel was first demonstrated in 1996 [5]. Since then, a number of prepare-and-measure as well as entanglement based schemes have been implemented in free space; the longest distance so far achieved on Earth is 144 km [6,7]. Nowadays, even quantum communication between earth and space is being conceived [8][9][10][11][12][13][14]. All of the systems so far referred to here have one major aspect in common: they are based on discrete quantum variables and use single photon threshold ('click') detectors, which involves spatial, spectral and/or temporal filtering in order to reduce background noise (see e.g. [15,16] for the first point-to-point demonstrations of free-space QKD in daylight).As already shown by Bennett [17], any two non-orthogonal quantum states suffice to ensure secure key distribution. This paved the way for continuous-variable (CV) protocols (for a review see [18,19]), based on a different approach: performing homodyne measurements on weak coherent states with the help of a bright local oscillator (LO). Generally, homodyne detectors offer immunity to st...

Digital signatures guarantee the authorship of electronic communications. Currently used "classical" signature schemes rely on unproven computational assumptions for security, while quantum signatures rely only on the laws of quantum mechanics to sign a classical message. Previous quantum signature schemes have used unambiguous quantum measurements. Such measurements, however, sometimes give no result, reducing the efficiency of the protocol. Here, we instead use heterodyne detection, which always gives a result, although there is always some uncertainty. We experimentally demonstrate feasibility in a real environment by distributing signature states through a noisy 1.6 km free-space channel. Our results show that continuous-variable heterodyne detection improves the signature rate for this type of scheme and therefore represents an interesting direction in the search for practical quantum signature schemes. For transmission values ranging from 100% to 10%, but otherwise assuming an ideal implementation with no other imperfections, the signature length is shorter by a factor of 2 to 10. As compared with previous relevant experimental realizations, the signature length in this implementation is several orders of magnitude shorter. DOI: 10.1103/PhysRevLett.117.100503 Digital signatures [1] are ubiquitous in electronic communication, used in, for example, Email and digital banking. They guarantee the provenance, integrity, and transferability of messages. Currently used classical digital signature schemes, however, rely on unproven computational assumptions [2], and may become insecure especially if quantum computers can be built [3]. Quantum digital signatures (QDSs) [4][5][6][7][8][9][10], on the other hand, give information-theoretic security [7], loosely speaking based on the fact that nonorthogonal quantum states cannot be perfectly distinguished from each other.The first quantum signature schemes assumed tamperproof, "authenticated" quantum communication links. Intuitively, this could be accomplished using parameter estimation techniques similar to those used in quantum key distribution (QKD). How to achieve this was explicitly shown only recently [10,11]. In addition, recent quantum signature schemes [6,9], including our protocol, do not require long-term quantum memory. Importantly, this means that quantum signatures can be implemented with current technology, essentially similar to QKD setups. "Classical" signature schemes with information-theoretic security also exist [12][13][14], but rely on secret shared keys, which could be accomplished using QKD. Quantum signature schemes may have some advantages over schemes relying on shared keys generated using QKD. In particular, the quantum bit error threshold for a signature scheme is in practice less strict than for distilling a secret shared key [11]. In addition, the required postprocessing is less demanding. Exactly what signature schemes are the most efficient, however, remains an open problem.Note that most QDS protocols, including this one, use quantu...