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Quantum Computing, Communication, and Simulation

Leveraging high-dimensional qudits for quantum communication and computation

Yaron Bromberg, Ohad Lib

Published Mar 5, 2026• 0 citations
Publisher

Abstract

Photons can carry quantum information not only in two-level systems (qubits) but also in d-level systems known as qudits. A single photon distributed across d optical modes can encode up to log2(d) qubits of information, allowing for more efficient use of quantum resources and increased resilience to noise. This advantage, however, comes at a price: implementing quantum gates and performing measurements in high-dimensional Hilbert spaces is significantly more demanding than in the qubit case. To tackle these challenges, I will present our recent work developing new protocols and optical hardware that enable quantum communication and computation with high-dimensional qudits encoded in the temporal or spatial modes of single and entangled photons. I will discuss our experimental implementations of quantum key distribution using weak coherent pulses [Sulimany et al., NPJ Quantum Information 11, 16 (2025)], single photons from quantum dots [Halevi et al., Optica Quantum 2, 351 (2024)], and entangled photon pairs [Lib et al., Optica Quantum 3, 182 (2025)]. In the latter, we demonstrated projective measurements in two mutually unbiased bases for $d = 25$ using a multi-plane light converter (MPLC). I will also show how the same MPLC platform can be used to perform elementary operations in measurement-based quantum computation with high-dimensional cluster states [Lib and Bromberg, Nat. Photonics 18, 1218 (2024)]. Throughout the talk, I will discuss the tradeoffs between qubit- and qudit-based approaches and highlight the regimes where high-dimensional systems offer a practical advantage.

DOI
10.1117/12.3091855

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Photons can carry quantum information not only in two-level systems (qubits) but also in d-level systems known as qudits. A single photon distributed across d optical modes can encode up to log2(d) qubits of information, allowing for more efficient use of quantum resources and increased resilience to noise. This advantage, however, comes at a price: implementing quantum gates and performing measurements in high-dimensional Hilbert spaces is significantly more demanding than in the qubit case. To tackle these challenges, I will present our recent work developing new protocols and optical hardware that enable quantum communication and computation with high-dimensional qudits encoded in the temporal or spatial modes of single and entangled photons. I will discuss our experimental implementations of quantum key distribution using weak coherent pulses [Sulimany et al., NPJ Quantum Information 11, 16 (2025)], single photons from quantum dots [Halevi et al., Optica Quantum 2, 351 (2024)], and entangled photon pairs [Lib et al., Optica Quantum 3, 182 (2025)]. In the latter, we demonstrated projective measurements in two mutually unbiased bases for d=25d = 25d=25 using a multi-plane light converter (MPLC). I will also show how the same MPLC platform can be used to perform elementary operations in measurement-based quantum computation with high-dimensional cluster states [Lib and Bromberg, Nat. Photonics 18, 1218 (2024)]. Throughout the talk, I will discuss the tradeoffs between qubit- and qudit-based approaches and highlight the regimes where high-dimensional systems offer a practical advantage.
The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.
The ability to prepare, control, and detect high-dimensional photonic quantum states is a key capability in modern quantum science. Spatially structured single- and bi-photon states provide access to large Hilbert spaces, enabling both fundamental studies and practical advances across quantum technologies. Precise control of these states is essential to characterising quantum light sources and to using spatial degrees of freedom for information encoding, with applications ranging from quantum imaging and simulation to high-capacity, noise-resilient quantum communication. In this talk, I will review recent experimental and theoretical progress in structured-light quantum information processing. I will discuss high-dimensional QKD with structured photons, strategies based on adaptive optics and tailored measurements to counter channel distortions, and protocols that exploit spatial mode structure. I will also describe how structured photonic states can be used to simulate linear and cyclic quantum systems, illustrating their potential as scalable platforms for high-dimensional quantum information processing.
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.
Photonics is a sophisticated platform for the development of novel quantum technologies, from quantum processors to distributed quantum communication. Most linear optical architectures focus on encoding qubits into photons using, for example, polarization or a dual-rail approach. However, encoding higher-dimensional systems - qudits - can in principle provide improved information capacity and noise tolerance in communication, and lower error thresholds in fault-tolerant quantum computation. Here we present new schemes for generating high-dimensional photonic entanglement and discuss how to build cluster states for universal high-dimensional quantum computation.
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.
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.