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Journal of the Optical Society of America B

High-dimensional cryptography with spatial modes of light: tutorial

Eileen Otte, Isaac M. Nape, Carmelo Rosales‐Guzmán, Cornelia Denz, Andrew Forbes, Bienvenu I. Ndagano

Published Aug 17, 2020• 77 citations
Publisher

Abstract

Fast and secure sharing of information is among the prime concerns of almost any communication system. While commonly used cryptographic algorithms cannot provide unconditional security, high-dimensional (HD) quantum key distribution (QKD) offers an exceptional means to this end. Here, we provide a tutorial to demonstrate that HD QKD protocols can be implemented in an effective way using optical elements that are known to most optics labs. We use spatial modes of light as our HD basis and show how to simulate QKD experiments with bright classical light, fostering its easy implementation for a more general audience including industry laboratories or laboratory classes in university teaching and in advanced laboratories for validation purposes. In particular, we use orbital angular momentum Bessel–Gaussian modes for our HD QKD demonstration to illustrate and highlight the benefits of using spatial modes as their natural Schmidt basis and self-healing feature.

DOI
10.1364/josab.399290

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Fast and secure sharing of information is among the prime concerns of almost any communication system. While commonly used cryptographic algorithms cannot provide unconditional security, high-dimensional (HD) quantum key distribution (QKD) offers an exceptional means to this end. Here, we provide a tutorial to demonstrate that HD QKD protocols can be implemented in an effective way using optical elements that are known to most optics labs. We use spatial modes of light as our HD basis and show how to simulate QKD experiments with bright classical light, fostering its easy implementation for a more general audience including industry laboratories or laboratory classes in university teaching and in advanced laboratories for validation purposes. In particular, we use orbital angular momentum Bessel–Gaussian modes for our HD QKD demonstration to illustrate and highlight the benefits of using spatial modes as their natural Schmidt basis and self-healing feature.
High-dimensional quantum key distribution (HD-QKD) enhances information efficiency and noise tolerance by encoding data in large Hilbert spaces. The orbital angular momentum (OAM) of light provides a scalable basis for such encoding and supports high-dimensional photonic communication. Practical OAM-based implementations remain constrained by challenges in state generation, transmission, and detection. This survey offers a consolidated overview of OAM-encoded HD-QKD, outlining fundamental principles, representative experiments, and system-level limitations. Recent progress in hybrid encodings, mode sorting, adaptive optics, and TF, CV, MDI, and DI frameworks is summarized with emphasis on practical feasibility.
Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon's spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.
A new implementation of high-dimensional quantum key distribution (QKD) protocol is discussed. Using three mutual unbiased bases, we present a d-level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.
High-dimensional quantum key distribution (HD-QKD) provides notable advantages over qubit-based QKD, including higher key rates and greater noise resilience. Leveraging the orbital angular momentum states of structured photons to encode information has become a prominent method for implementing HD-QKD. However, practical challenges such as state-dependent diffraction, limited receiving aperture, and atmospheric turbulence impose constraints on the attainable performance and encoding dimension of QKD in free-space links. In this work, we address these challenges with focused, structured photons. Numerical simulations indicate that this method markedly enhances transmission efficiency and improves the robustness against turbulence, resulting in higher key rates and extended transmission distances in free-space HD-QKD. Additionally, focused, structured photons allow us to implement higher-dimensional QKD and enable QKD systems to achieve superior performance with smaller receiving apertures in a turbulent free-space link. This makes our approach particularly advantageous for applications of unmanned aerial vehicles and satellite platforms. Our work contributes to exploring the robust QKD schemes employing structured photons and may promote its application in quantum networks.
Quantum key distribution (QKD) is an unconditionally secure way of sharing secret cryptographic keys on a public channel. Recently, high dimension QKD protocols have gained focus to achieve better security against various attack models. Here, we focus on the robustness of high dimensional QKD protocol against two realistic attack models, i.e. photon number splitting (PNS) attack and beam splitter (BS) attack. We present the high dimensional quantum key distribution system that incorporates a decoy-state scheme with complex structured light (OAM modes) using the KMB09 protocol. The complete QKD system design with experimental setup details and evaluation results are presented. The experimental results show that our proposed decoy-state scheme is robust against both PNS and BS attacks.
Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.