In this project we examine several different quantum key distribution protocols which we divide into ones utilizing qubits whose Hilbert spaces are two dimensional and ones whose Hilbert space dimension is greater than two, these units of data in quantum computers are known as qudits and in the papers we'll examine are implemented using the orbital angular momentum of twisted photons. In sections [3] and [4] the specific procedures of each protocol are briefly described and followed by an examination of the theoretical and experimental merits of each protocol. These merits are measured in the bit error rate tolerance $e_b$, which quantifies the maximum channel noise and the key rate $R$ which quantifies the rate at which data is transferred in the protocol. In section [7] we present a unified view of all the relevant data for the different protocols, and argue for the benefits and drawbacks of the different protocols for different applications.
In this project we examine several different quantum key distribution protocols which we divide into ones utilizing qubits whose Hilbert spaces are two dimensional and ones whose Hilbert space dimension is greater than two, these units of data in quantum computers are known as qudits and in the papers we'll examine are implemented using the orbital angular momentum of twisted photons. In sections [3] and [4] the specific procedures of each protocol are briefly described and followed by an examination of the theoretical and experimental merits of each protocol. These merits are measured in the bit error rate tolerance eb, which quantifies the maximum channel noise and the key rate R which quantifies the rate at which data is transferred in the protocol. In section [7] we present a unified view of all the relevant data for the different protocols, and argue for the benefits and drawbacks of the different protocols for different applications.
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.
Recently, Chau [Phys. Rev. A 92, 062324 (2015)] introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a 2n-dimensional Hilbert space in the form $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$ with $n\ensuremath{\ge}2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate n bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n\ensuremath{-}1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of n=2, the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.
Abstract High-dimensional quantum key distribution (QKD) based on entangled qudits has emerged as a promising route for advancing the performance and practicality of quantum communication. By extending beyond the qubit framework, qudit entanglement enables the encoding of multiple bits per particle and offers greater robustness against noise, loss, and eavesdropping. In this review, we present qudit-based entanglement QKD protocols and their experimental demonstrations. We first introduce the basic concepts of qudits and provide an overview of foundational qubit-based entanglement QKD schemes, such as Ekert '91 (E91) and Bennett–Brassard–Mermin '92 (BBM92), which establish the core principles of entanglement-based secure key generation. Subsequently, we examine the generalization of these protocols to entangled qudits, highlighting how higher dimensionality enhances secure key rates and noise tolerance. Finally, we survey experimental demonstrations of qudit-based entanglement QKD across photonic platforms and outline prospects, showing that high-dimensional entanglement can be reliably generated, distributed, and measured for QKD with high stability and scalability. Remarkably, these achievements not only verify the feasibility of practical high-dimensional QKD, but also demonstrate clear advantages over qubit-based systems. Overall, theoretical frameworks and experimental realizations reviewed here position photonic qudit-based entanglement QKD as a promising resource for scalable, high-speed, and secure quantum communication networks, unveiling its potential as a central component in the future of quantum information technologies.
The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations of Quantum Mechanics. Purpose of this review is to introduce qudits, to summarize their application to Quantum Communication and researches on Local Realism and, finally, to describe some recent experiment for realizing them. A Little more in details: after a short introduction, we will consider the advantages of testing local realism with qudits, discussing both the 3-4 dimensional case (both for maximally and non-maximally entanglement) and then the extension to an arbitrary dimension. Afterwards, we will discuss the theoretical results on using qudits for quantum communication, epitomizing the outcomes on a larger security in Quantum Key Distribution protocols (again considering separately qutrits, ququats and generalization to arbitrary dimension). Finally, we will present the experiments performed up to now for producing quantum optical qudits and their applications. In particular, we will mention schemes based on interferometric set-ups, orbital angular momentum entanglement and biphoton polarization. Finally, we will summarize what hyperentanglement is and its applications.
Quantum key distribution (QKD) protocols most often use two conjugate bases in order to verify the security of the quantum channel. In the majority of protocols, these bases are mutually unbiased to one another, which is to say they are formed from balanced superpositions of the entire set of states in the opposing basis. Here, we introduce a high-dimensional QKD protocol using qubit-like states, referred to as Fourier-qubits (or F-qubits). In our scheme, each F-qubit is a superposition of only two computational basis states with a relative phase that can take d distinct values, where d is the dimension of the computational basis. This non-mutually-unbiased approach allows us to bound the information leaked to an eavesdropper, maintaining security in high-dimensional quantum systems despite the states’ seemingly two-dimensional nature. By simplifying state preparation and measurement, our protocol offers a practical alternative for secure high-dimensional quantum communications. We experimentally demonstrate this protocol for a noisy high-dimensional QKD channel using the orbital angular momentum degree of freedom of light and discuss the potential benefits for encoding in other degrees of freedom. High dimensional quantum key distribution (QKD) systems will allow for higher key generation rate, but with added complexity for creating and detecting high dimensional quantum states. The authors demonstrate a QKD protocol using “qubit-like” qudit states, “F-qubits”, with simpler generation and detection, maintaining the benefits of high dimensional QKD protocols.
This paper presents a comprehensive review of quantum communication using photons, based primarily on the foundational work of Krenn, Malik, Scheidl, Ursin, and Zeilinger. The review covers core quantum mechanical principles such as qubits, superposition, entanglement, and the no-cloning theorem, and explains how these principles underpin secure quantum communication. Key protocols including Quantum Key Distribution (QKD) and quantum teleportation are discussed. The paper further explores long-distance ground-based and space-based experiments, and examines the emerging role of high-dimensional quantum states using Orbital Angular Momentum (OAM) of photons. The aim is to provide a structured understanding of the current state and future potential of quantum communication technologies.