High-dimensional intracity quantum cryptography with structured photons
Alicia Sit, Frédéric Bouchard, Robert Fickler, Jérémie Gagnon-Bischoff, Hugo Larocque, Khabat Heshami, Dominique Elser, Christian Peuntinger, Kevin Günthner, Bettina Heim, Christoph Marquardt, Gerd Leuchs, Robert W. Boyd, Ebrahim Karimi
Quantum key distribution (QKD) promises information-theoretically 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 [3-7]. 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.
Quantum key distribution (QKD) promises information-theoretically 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 [3-7]. 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.
Light with a complex amplitude structure invokes interesting fundamental properties such as phase and polarization singularities, which also enables novel applications in classical and quantum optical experiments [1]. One feature, namely a twisted phase front and its orbital angular momentum, attracted a lot of attention due its broad range of applications. In the quantum domain, structured photons are highly beneficial since they serve as a physical realizations of high-dimensional states, which allow for example an enlarged information content per single carrier and are known to have a better noise resistance in quantum cryptography applications [2]. At first, I will present a set of laboratory experiments, in which we investigate different quantum cryptographic protocols. Our versatile approach relies on a heralded single photon source, a preparation stage at Alice’s sender, a 1 m-long quantum channel, and a detection stage at Bob’s receiver unit. Because the generation and detection is performed using computer generated, re-programmable holograms displayed on spatial light modulators, the same setup can be used to experimentally survey different quantum key distribution techniques and compare their benefits and deficiencies. The investigated protocols are all based on high-dimensional quantum states and include the seminal protocol of Bennett & Brassard, tomographic protocols, and recently introduced differential phase shift protocols [3,4]. We compare the performance of the different approaches in terms of noise resistance and secret key rates. Our study highlights the benefits of using structured photons and high-dimensional quantum states for different implementations and channel conditions. In a second series of experiments, we get a step closer to real world implementations and investigate long distance and underwater quantum cryptography using high-dimensional quantum information encoded on structured light. We establish an approx. 280m long intra-city quantum link and study the influence of turbulence on achievable key rates [5]. We further test the effect of water turbulences on an underwater quantum channel using twisted photons in an outdoor pool of 3 m length [6]. Although we are able establish a secure channel with three dimensional quantum states, we find mode deformations and vortex splitting due to strong turbulent conditions most probably caused by local variations in temperature. We perform a detailed analysis of the observed turbulence and find that underwater channels may give rise to turbulent conditions that are fundamentally different in terms of temporal and spatial disturbance from those present in a free-space channel. [1] H. Rubinsztein-Dunlop et al. Roadmap on structured light, Journal of Optics 19, 013001 (2017) [2] M. Erhard, R. Fickler, M. Krenn, A. Zeilinger, Twisted Photons: New Quantum Perspectives in High Dimensions, Nature Light: Science & Applications, 7 17146 (2018) [3] F. Bouchard et al. Experimental investigation of quantum key distribution protocols with twisted photons, arXiv:1802.05773 [4] F. Bouchard, A. Sit, K. Heshami, R. Fickler, E. Karimi, Round-Robin Differential Phase-Shift Quantum Key Distribution with Twisted Photons, arXiv:1803.00166 [5] A. Sit et al. High-Dimensional Intra-City Quantum Cryptography with Structured Photons, Optica 4, 1006 (2017) [6] F. Bouchard et al. Underwater Quantum Key Distribution in Outdoor Conditions with Twisted Photons, arXiv:1801.10299
Optical fiber links and networks are integral components within and between cities' communication infrastructures. Implementing quantum cryptographic protocols on either existing or new fiber links will provide information-theoretical security to fiber data transmissions. However, there is a need for ways to increase the channel bandwidth. Using the transverse spatial degree of freedom is one way to transmit more information and increase tolerable error thresholds by extending the common qubit protocols to high-dimensional quantum key distribution (QKD) schemes. Here we use one type of vortex fiber where the transverse spatial modes serves as an additional channel to encode quantum information by structuring the spin and orbital angular momentum of light. In this proof-of-principle experiment, we show that two-dimensional structured photons can be used in such vortex fibers in addition to the common two-dimensional polarization encryption, thereby paving the path to QKD multiplexing schemes.
It has been widely recognized that the underlying principles of quantum mechanics could be used to enable secure communications, without any additional conventional cryptographic systems, while utilizing the properties of the photons. Considerable research efforts have been invested to develop an efficient quantum key distribution (QKD) scheme over either free-space optical or fiber-optics channels. Most of these research efforts have been focused on a two-dimensional QKD, commonly realized by the use of the polarization state of photons. However, the data rates for the quantum key exchange in two-dimensional QKD are still low, while transmission distance is limited. On the other hand, it is well known that photons can carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM), associated with the polarization and azimuthal phase of the complex electric field, respectively. Accordingly, we can define the combined-OAM-SAM state of a photon as |l, σ〉, where l and σ correspond to OAM and SAM indexes, respectively. Since the OAM eigenstates are orthogonal, an arbitrary number of bits per single photon can be transmitted, which could considerably increase the total secure bit rate. To improve secure data rates, we propose two types of protocols, namely, nonentangled-based (such as weak coherent state) and entanglement-assisted protocols, both employing the photon combined-OAM-SAM state, which can be used for secure key distribution over free-space optical and few-mode fiber channels. Two types of entanglement-assisted protocols are described, namely, two-basis and (D + 1)-basis protocols ( D is dimensionality of corresponding Hilbert space). We further describe how to implement the qudit gates required for implementation of these protocols. Finally, we discuss the security issues of the proposed protocols and determine both infinite and finite secret key fraction rates.
Quantum Key Distribution (QKD) guarantees the security of communication with quantum physics. Most of widely adopted QKD protocols currently encode the key information with binary signal format---qubit, such as the polarization states. Therefore the transmitted information efficiency of the quantum key is intrinsically upper bounded by 1 bit per photon. High dimensional quantum system is a potential candidate for increasing the capacity of single photon. However, due to the difficulty in manipulating and measuring high dimensional quantum systems, the experimental high dimensional QKD is still at its infancy. Here we propose a sort of practical high-speed high dimensional QKD using partial mutual unbiased basis (PMUB) of photon's orbital angular momentum (OAM). Different from the previous OAM encoding, the high dimensional Hilbert space we used is expanded by the OAM states with same mode order, which can be extended to considerably high dimensions and implemented under current state of the art. Because all the OAM states are in the same mode order, the coherence will be well kept after long-distance propagation, and the detection can be achieved by using passive linear optical elements with very high speed. We show that our protocol has high key generation rate and analyze the anti-noise ability under atmospheric turbulence. Furthermore, the security of our protocol based on PMUB is rigorously proved. Our protocol paves a brand new way for the application of photon's OAM in high dimensional QKD field, which can be a breakthrough for high efficiency quantum communications.
This thesis encompasses a body of experimental work on the use of structured light in quantum cryptographic protocols. In particular, we investigate the ability to perform quantum key distribution through various quantum channels (fibre, free-space, underwater) in laboratory and realistic conditions. We first demonstrate that a special type of optical fibre (vortex fibre) capable of coherently transmitting vector vortex modes is a viable quantum channel. Next, we describe the first demonstration of high-dimensional quantum cryptography using structured photons in an urban setting. In particular, the prevalence of atmospheric turbulence can introduce many errors to a transmitted key; however, we are still able to transmit more information per carrier using a 4-dimensional scheme in comparison to a 2-dimensional one. Lastly, we investigate the possibility of performing secure quantum communication with twisted photons in an uncontrolled underwater channel. We find that though it is possible for low-dimensional schemes, high-dimensional schemes suffer from underwater turbulence without the use of corrective wavefront techniques.
Abstract In the last two decades, structured light patterns with orbital angular momentum (OAM) have been extensively utilized in quantum cryptography or quantum key distribution, which is generally considered an unconditionally secure method of secret key transmission between two distant communicating entities. High-dimensional encoding of quantum bits in quantum key distribution improves the security and information-carrying capability of a quantum signal. Significant degradation in the efficiency of such communication is observed due to the aberration of OAM states under atmospheric turbulence. In this paper, we focus on analyzing the impact of atmospheric turbulence on the error-rates of quantum key distribution, which is considered the benchmark in analyzing the security of such communication over the quantum channel in the presence of an intruder (man-in-the-middle). Our results show that turbulence under normal conditions does not significantly affect the successful transmission of secret quantum bits between sender and receiver. Furthermore, we identify an interesting variation in the signature of error-rates to clearly detect the presence of an intruder as a result of medium-level turbulence.