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.
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.
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.
Qudits, the d-dimensional extension of qubits, open new perspectives in several fields, from fundamental quantum mechanics to quantum cryptography. Although photon polarization is a privileged choice for qubits encoding, it is not suitable for the physical realization of qudits. However, in order to realize multidimensional quantum systems, other degrees of freedom of single photons such as path or orbital angular momentum are available. When two or more degrees of freedom are exploited simultaneously we refer to "hybrid encoding". It is possible for instance to encode information in a four dimensional (ququart) hybrid space spanned by polarization and a bidimensional orbital angular momentum subspace of a single photon. Here we present how high dimensional hybrid systems can be exploited to overcome a major limitation of quantum communication: the need of a shared reference frame. Indeed the joint action of polarization and orbital angular momentum of hybrid ququarts can be exploited to realize quantum communication without a shared reference frame. We experimentally showed that, by using a proper subspace of hybrid ququart space, it is possible to perform any quantum communication protocol and violate CHSH inequalities without any information about the reference frame orientation of the two parties (except the direction of propagation of the photons). Such feature could find application in satellite based communication schemes.
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.
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.
Superposition of optical coherent states ∣±α⟩, possessing opposite phases, play an important role as qubits in quantum information processing (QIP) tasks and are of fundamental importance in testing quantum mechanics. Passage of such superposition of coherent states (SCS) from a 50:50 beam splitter lead to generation of entangled coherent states. Recently, ququats and qutrits defined in four and three dimensional Hilbert space respectively, have attracted much attention as they offer advantage in secure quantum communication. However, practical utilization of these advantages essentially require physical realization of quantum optical ququats and qutrits. Here, we define four new multi-photonic states (MPS) with 4n+j (here, j=0,1,2 or 3, and n=0,1,...,∞) numbers of photon and show how the SCS can be used to encode ququat using these MPS as basis vectors of a four dimensional Hilbert space. When these MPS fall upon a 50:50 beam splitter, the resulting states are bipartite four-component entangled coherent states (BFECS) equivalently representing the entangled ququats. We briefly discuss the photon statistical properties of such MPS and BFECS. We show that these MPS and BFECS can be synthesized using even coherent states as input to an interferometer. We give a simple linear optical protocol for almost perfect teleportation of a ququat encoded in SCS with the aid of BFECS as quantum channel. We also describe how these ququats can be used for realization of higher dimensional BB84 protocol in order to increase the security of quantum key distribution. Finally, we discuss the possible advantages of using SCS as ququats and BFECS as quantum channel in different QIP tasks.
Abstract In recent years, there has been a rising interest in high‐dimensional quantum states and their impact on quantum communication. Indeed, the availability of an enlarged Hilbert space offers multiple advantages, from larger information capacity and increased noise resilience, to novel fundamental research possibilities in quantum physics. Multiple photonic degrees of freedom have been explored to generate high‐dimensional quantum states, both with bulk optics and integrated photonics. Furthermore, these quantum states have been propagated through various channels, for example, free‐space links, single‐mode, multicore, and multimode fibers, and also aquatic channels, experimentally demonstrating the theoretical advantages over 2D systems. Here, the state‐of‐the‐art on the generation, propagation, and detection of high‐dimensional quantum states is reviewed. Quantum communication with states living in d ‐dimensional Hilbert spaces, qudits, yields great benefits. However, qudits generation, transmission, and detection is not a simple task to accomplish. This review presents the state‐of‐the‐art on the generation, propagation, and measurement of high‐dimensional quantum states, highlighting their advantages, issues, and future perspectives.