We report the generation and distribution of frequency-entangled qudits with high dimensions over a 0.77-km fiber network via hybrid quantum interference. The qudits exhibit 98% two-photon visibility, demonstrating high entanglement and robustness for practical applications.
High-dimensional (HD) quantum entanglement expands the Hilbert space, offering a robust framework for quantum information processing with enhanced capacity and error resilience. In this work, we present an HD frequency-domain entangled state, the hybrid frequency-entangled qudit (HFEQ), generated via Hong-Ou-Mandel (HOM) interference, exhibiting both discrete-variable (DV) and continuous-variable (CV) characteristics in the frequency domain. By tuning HOM interference, we generate and control HFEQs with dimensions D = 5 , 7 , 9 , and 11, confirming their DV nature. Franson interferometry verifies global frequency correlations with a visibility of 97.6 ± 0.6 % and CV entanglement within individual frequency modes with a visibility exceeding 95 % . Furthermore, based on the developed theoretical model, the generated HFEQs exhibit a Schmidt number that exceeds the upper bound D of conventional frequency-entangled qudits, certifying additional entanglement inherent to the hybrid structure. Our findings provide deeper insight into the physical nature of frequency-entangled qudits generated by quantum interference and introduce a resource for HD time-frequency quantum information processing.
Frequency modes of light are one of the most promising platforms that provide access to high-dimensional quantum states amongst different photonic degrees of freedom capable of high-dimensionality, enabling robust, error-tolerant, and scalable quantum optical information systems. We demonstrate engineering of precisely controlled two-photon high-dimensional states entangled in frequency through time-domain Fourier optical synthesis. We generate and convert a continuous broadband frequency-entangled state into a large range of discrete frequency bins suitable for ITU standards, with spacings ranging from 12.5 GHz to 750 GHz, and observe spectral anticorrelations over 38 frequency bins, including intra-bin pure states at a 100 GHz bin spacing. We characterize the full quantum state dimensionality via Schmidt decomposition and observe lower bounds on the frequency-binned Hilbert-space dimensionalities of at least 289, formed by two entangled qudits with dimension 17. Furthermore, we demonstrate quantum nonlocality via frequency correlations in a transmission experiment over a campus-scale two-node fiber network. This work represents a crucial step towards building a versatile and relatively simple way of generating precisely controlled high-dimensional spectral qudits, with the potential of harnessing in wavelength-multiplexed quantum networks, high-dimensional information processing, and communication of quantum states specifically, and fiber-optic quantum remote sensing.
High-dimensional, frequency-entangled photonic quantum bits (qudits for d -dimension) are promising resources for quantum information processing in an optical fiber network and can also be used to improve channel capacity and security for quantum communication. However, up to now, it is still challenging to prepare high-dimensional frequency-entangled qudits in experiments, due to technical limitations. Here we propose and experimentally implement a novel method for a simple generation of frequency-entangled qudts with without the use of any spectral filters or cavities. The generated state is distributed over 15 km in total length. This scheme combines the technique of spectral engineering of biphotons generated by spontaneous parametric down-conversion and the technique of spectrally resolved Hong-Ou-Mandel interference. Our frequency-entangled qudits will enable quantum cryptographic experiments with enhanced performances. This distribution of distinct entangled frequency modes may also be useful for improved metrology, quantum remote synchronization, as well as for fundamental test of stronger violation of local realism.
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.
In the quest to realize a scalable quantum network, semiconductor quantum dots (QDs) offer distinct advantages, including high single-photon efficiency and indistinguishability, high repetition rate (tens of gigahertz with Purcell enhancement), interconnectivity with spin qubits, and a scalable on-chip platform. However, in the past two decades, the visibility of quantum interference between independent QDs rarely went beyond the classical limit of 50%, and the distances were limited from a few meters to kilometers. Here, we report quantum interference between two single photons from independent QDs separated by a 302 km optical fiber. The single photons are generated from resonantly driven single QDs deterministically coupled to microcavities. Quantum frequency conversions are used to eliminate the QD inhomogeneity and shift the emission wavelength to the telecommunication band. The observed interference visibility is 0.67 ± 0.02 (0.93 ± 0.04) without (with) temporal filtering. Feasible improvements can further extend the distance to ∼600 km. Our work represents a key step to long-distance solid-state quantum networks.