A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channels tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.
A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channels tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the propagation photon with an arbitrary complex wavefront in a material with an isotropic but inhomogeneous index of refraction. We simulate the waveform propagation of an optical vortex in a volume holographic element in the paraxial approximation using an operator splitting method. We use this code to analyze an OAM volume-holographic sorter. Furthermore, there are analogue models of the evolution of a wavefront in the curved spacetime environs of the Earth that can be constructed using an optical medium with a given index of refraction. This can lead to a work-bench realization of a satellite HD-QKD system.
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.
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.
High-dimensional, discrete quantum states, also known as qudits, offer several advantages over their two- dimensional counterpart (qubits). For example, in quantum communication, the use of qudits not only increases the amount of information encoded into a single carrier, but also enhances the security of quantum key distribution (QKD) protocols. In particular, in entanglement-based QKD the intervention of an eavesdropper can be excluded by the violation of a Bell-type inequality, which is the more violated the larger the dimensionality of the employed states. Spanning a discrete infinite-dimensional Hilbert space, the orbital angular momentum (OAM) of light can be used to realize such high-dimensional quantum systems. Moreover, the non-linear process of spontaneous parametric down conversion naturally provides biphoton states entangled in a large number of OAM modes. However, the defining feature of photons carrying OAM, namely their helical phase front, is strongly perturbed by disturbances along the light propagation path. In this thesis, we study how different perturbations influence OAM entanglement, and how we can counteract their detrimental effects. We first consider the entanglement losses induced by diffraction on obstructions or apertures. In this setting, we derive an analytical expression for the entanglement losses depending only on the overlap between the diffracted images of the OAM modes used to encode the entanglement. With the help of this expression, we investigate the role of the radial structure of the encoding modes in mitigating entanglement losses due to diffraction. In particular, we show that entanglement encoded in multi-ring Bessel-Gaussian modes is more resilient against diffraction than that encoded into single ring Laguerre-Gaussian modes. Moreover, using the uncertainty relation for angular position and angular momentum, we demonstrate that the entanglement of a biphoton state, with well defined OAM, past a "cake-slice" aperture is a universal function of the product of the angular uncertainty defined by the aperture and of the OAM of the encoding modes. The use of OAM entanglement in free-space quantum communication is severely limited by phase distortions introduced by random refractive index fluctuations due to atmospheric turbulence. In this dissertation, we discuss the efficiency of adaptive optics (AO) in mitigating turbulence-induced OAM entanglement losses, for a vast range of atmospheric conditions. In particular, we show that the stronger Bell correlations available in higher dimensions are nullified by their faster turbulence-induced decay. In contrast, AO corrections allow to restore non-locality, and thus the security of entanglement-based quantum communication, even for high-dimensional states under moderate turbulence. In many practical situations, high-dimensional states are encoded in a subspace of a large (eventually infinite-dimensional) Hilbert space. Moreover, even though the dynamical evolution of the system couples the encoding subspace to the complement of the Hilbert space, the evolved states are often projected (truncated) into a smaller subspace, because of experimental restrictions such as limited detector size or resolution. With the help of numerically generated random unitary matrices, we obtain an expression for truncation-induced entanglement losses as a function of the dimensions of the total, encoding and truncation Hilbert spaces. Finally, we present a first endeavour towards a fully quantum description of light propagation through atmospheric turbulence. In particular, we derive a quantized Hamiltonian that governs the behaviour of monochromatic paraxial photons in a random, non-homogeneous dielectric medium. Our Hamiltonian is expressed in terms of creation and annihilation operators of photons populating OAM modes, where the turbulence-induced mixing of several different modes is described by an appropriate coupling term.
The nondiffracting higher-order Bessel beams carry the orbital angular momentum(OAM). During free propagation,their transverse intensity profile remains nearly invariant in a range.The beam comprises the topological charge l helical phasefronts and carries an orbital angular momentum of lh per photon.The angular momentum number carried by the photon in each eigenmode is represented by l, and the eigenstates |l〉can generate multidimensional quantum entangled states.A method of optical communication is presented that encodes information in two orthogonal orbital angular momentum states based on higher-order Bessel beams.Each photon carries OAM states of information,which can increase the key generation rate of the protocol,and offer a quantum solution for increase of the optical communication distance.
In this thesis, Quantum Key Distribution and quantum communication methods based on high-dimensional spatial coding of light are developed. Their security is based on the fundamental quantum nature of light and profits from the highdimensional Hilbert spaces offered intrinsically by imaging optics. An overview of classical information theory and quantum information is given to introduce the field of quantum cryptography. The advantages of larger dimensional alphabets and the security of the standard two-bases BB84 protocol is shown. The spatial states used for encoding are introduced. An analytic expression for the upper bound on the mutual information for these states is derived, including multiphoton states, detector noise and beam broadening. High-dimensional encoding of single photons is experimentally realized, reaching 10.5 bit per received photon. The dependence of the mutual information on the number of detector pixels is discussed and the experimental values are compared with the theoretical upper bound. It was shown that a standard error-correcting LDPC code is sufficient to achieve practically error-free communication. By adding a second mutually unbiased basis, a large-alphabet QKD system is experimentally realized and characterized. The security of this BB84-like protocol is analyzed in terms of intercept-resend and collective attacks. The key rate after postprocessing is analyzed under realistic circumstances, including finite key length. Finally, a new quantum communication method is demonstrated, which is based on encoding information into wavefronts decomposed over guided modes of a multimode fiber. At the end a step back is made and the similarities and differences of several quantum authentication and quantum cryptography schemes as well as Quantum Data Locking are discussed. This involves comparison of the characteristics of the classical channel, the quantum channel and the necessary dimension of the Hilbert space.
Orbital angular momentum (OAM) states of photons span a high-dimensional Hilbert space, and by using it, higher information capacity and enhanced security can be achieved for both classical communication and quantum key distribution. In this work, we propose a feasible basis-independent encoding scheme for OAM states and show its application in high-dimensional quantum secure direct communication, which enables direct transmission of meaningful messages, in addition to random secret key establishing. Imperfections of optical components may reduce the efficiency of the encoding scheme and, thus, the channel capacity. We discuss the optimal input distribution under realistic conditions to achieve maximal mutual information and an alternative solution using a different set of mutually unbiased bases in the case of a prime-dimensional quantum system.