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Quantum Nanophotonic Materials, Devices, and Systems

Generation of high-dimensional photonic entanglement

Alex E. Jones, Stefano Paesani, Jacob F. F. Bulmer, Raffaele Santagati, Anthony Laing

Published Jul 30, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2598853

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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.
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.
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.
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from 50%50\%50% to 1−1/d1-1/d1−1/d for qudits of dimension ddd without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.
Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.
Photonic entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Optical satellite links allow transmitting entangled photons over longer distances than currently possible on ground and could provide a path towards global quantum communication networks. The majority of current photonic free-space quantum communication systems, including two recent quantum satellite experiments, use two-dimensional polarization encoding, where each photon can carry at most a single bit of quantum information. Encoding additional qubits in the high-dimensional spatio-temporal degrees of freedom could not only increase channel capacities but also improve robustness with respect to noise and eavesdropping in quantum cryptography. Here, we give an overview of our efforts towards exploiting high-dimensional entanglement in long-distance free-space quantum communications. We report on the results of a first feasibility study, in which we used polarization / energy-time hyperentanglement to increase the dimensionality of the state space and transmit genuine 4-dimensional entanglement via an intra-city free-space link. We discuss how we intend to extend this approach to applications in noise-tolerant large-alphabet quantum key distribution via free-space links, and, ultimately, experiments with satellites.