We investigate various high-dimensional quantum cryptographic protocols using twisted photons and their feasibility in realistic conditions. In particular, we perform quantum key distribution in an intra-city freespace link and an underwater channel.
Over the last few decades, quantum cryptography has been one of the most important quantum technologies developed. It holds the promise of communicating secure information over untrusted channels. In particular, quantum cryptography is immune to the eventual threats posed by large-scale quantum computers, which is not the case for our current classical cryptography infrastructures. In a world where information, communication and privacy are of paramount importance, the development of secure quantum communication infrastructures becomes imperative. So far, most of the quantum cryptographic systems developed to date are based on two-dimensional encoding schemes, analogous to classical bits, known as qubits. Nevertheless, other than for the polarization of light, photonic degrees of freedom, i.e. position, momentum, time and frequency, naturally occur as high-dimensional quantum systems. Moreover, by considering high-dimensional encoding schemes beyond qubits, advantages in terms of information capacity and noise tolerance are predicted in theory. In this thesis, the basic components of a high-dimensional quantum cryptographic system are investigated. We begin by reviewing important developments in quantum cryptography and high-dimensional quantum information. As a starting point, two different quantum information tasks, i.e. optimal quantum cloning and quantum metrology, are experimentally investigated for high-dimensional quantum systems in order to demonstrate the numerous advantages of performing quantum tasks beyond qubits. The photonic degree of freedom used in these experiments, known as transverse spatial modes, is obtained by combining the position and momentum photonics degrees of freedom. Thus, we develop a novel method to measure high-dimensional quantum states encoded in arbitrary spatial modes. Using a similar characterization technique, several high-dimensional quantum communication channels are characterized to perform high-dimensional quantum cryptography. The tools developed in the laboratory are then brought to realistic conditions in order to test the feasibility of high-dimensional quantum cryptography. Two different types of quantum channels are experimentally investigated, namely an intra-city 300 m long free-space link and a short 3 m outdoor underwater link. Finally, we investigate and compare novel high-dimensional protocols to overcome current limitations.
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
Quantum key distribution is on the verge of real world applications, where perfectly secure information can be distributed among multiple parties. Several quantum cryptographic protocols have been theoretically proposed and independently realized in different experimental conditions. Here, we develop an experimental platform based on high-dimensional orbital angular momentum states of single photons that enables implementation of multiple quantum key distribution protocols with a single experimental apparatus. Our versatile approach allows us to experimentally survey different classes of quantum key distribution techniques, such as the 1984 Bennett & Brassard (BB84), tomographic protocols including the six-state and the Singapore protocol, and to investigate, for the first time, a recently introduced differential phase shift (Chau15) protocol using twisted photons. This enables us to experimentally compare the performance of these techniques and discuss their benefits and deficiencies in terms of noise tolerance in different dimensions.
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.
Quantum cryptography has emerged as a rapidly advancing field in recent years and represents one of the first practical applications of quantum physics beyond purely theoretical research. Despite its potential, current quantum cryptographic systems remain highly sensitive to noise. High- dimensional implementations offer a promising strategy to en- hance robustness. In this work, we investigate high-dimensional quantum key distribution protocols. Particular emphasis is placed on maritime communication scenarios, where harsh environ- mental conditions, atmospheric turbulence, and platform motion introduce significant noise and instability.