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Applied Sciences

High-Dimensional Quantum Key Distribution with N-Qudits States in Optical Fibers

Jesús Liñares, Xesús Prieto-Blanco, Alexandre Vázquez-Martínez

Published Jan 29, 2026• 0 citations
Publisher

Abstract

We present a high-dimensional quantum key distribution protocol by using N-qudits quantum light states, that is, product states with N photons, each of them in a quantum superposition of dimension d which provides a high dimension dN and accordingly a very high security. We present the implementation of this protocol in different types of optical fibers where the mentioned states undergo perturbations under propagation in optical fibers; such perturbations can be notably reduced in a passive (autocompensation) or active way and importantly the N-qubits present a great robustness against such optical perturbations. Likewise, quantum states also undergo attenuation, that is, some photons are lost under propagation in the optical fibers and then effective N′ (< N)-qudits are obtained which also are used to generate secret keys. In fact, the detection of states combines standard projective measurements along with photon coincidences. Besides, we analyze the security of this high-dimensional protocol under an intercept and resend attack realized by Eve, and the resulting secure key rates are calculated showing a significative increasing with the dimension provided by the number N of photons.

DOI
10.3390/app16031396

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We present a high-dimensional quantum key distribution protocol by using N-qudits quantum light states, that is, product states with N photons, each of them in a quantum superposition of dimension d which provides a high dimension dN and accordingly a very high security. We present the implementation of this protocol in different types of optical fibers where the mentioned states undergo perturbations under propagation in optical fibers; such perturbations can be notably reduced in a passive (autocompensation) or active way and importantly the N-qubits present a great robustness against such optical perturbations. Likewise, quantum states also undergo attenuation, that is, some photons are lost under propagation in the optical fibers and then effective N′ (< N)-qudits are obtained which also are used to generate secret keys. In fact, the detection of states combines standard projective measurements along with photon coincidences. Besides, we analyze the security of this high-dimensional protocol under an intercept and resend attack realized by Eve, and the resulting secure key rates are calculated showing a significative increasing with the dimension provided by the number N of photons.
We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against collective attacks. The protocol, which represents a QKD analog of pulse position modulation, is compatible with standard fiber telecommunications channels and wavelength division multiplexers. We describe several physical implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at >4>4>4 bits per character of distilled key across over 200 km of fiber.
In this work we present a high-dimensional discrete modulated CV-QKD protocol, with dimension , in optical fibers, where is the number of optical modes. We use -dimensional product states of weak coherent states that undergo perturbations along optical fibers and that are cancelled in a passive way (autocompensation) and then measured by a standard balanced homodyne detection. We analyze the security of this high-dimensional protocol under two types of attack. First, an intercept and resend attack implemented with simultaneous homodyne measurement in both quadratures. Then, a beam-splitter attack with channel substitution is also considered. Finally, the resulting secure key rates are calculated showing a significative increase with dimension.
Quantum key distribution (QKD) is a secure communication scheme for sharing symmetric cryptographic keys based on the laws of quantum physics, and is considered a key player in the realm of cyber-security. A critical challenge for QKD systems comes from the fact that the ever-increasing rates at which digital data are transmitted require more and more performing sources of quantum keys, primarily in terms of secret key generation rate. High-dimensional QKD based on path encoding has been proposed as a candidate approach to address this challenge. However, while proof-of-principle demonstrations based on lab experiments have been reported in the literature, demonstrations in realistic environments are still missing. Here we report the generation of secret keys in a 4-dimensional hybrid time-path-encoded QKD system over a 52-km deployed multicore fiber link forming by looping back two cores of a 26-km 4-core optical fiber. Our results indicate that robust high-dimensional QKD can be implemented in a realistic environment by combining standard telecom equipment with emerging multicore fiber technology.
Quantum key distribution (QKD) is an unconditionally secure way of sharing secret cryptographic keys on a public channel. Recently, high dimension QKD protocols have gained focus to achieve better security against various attack models. Here, we focus on the robustness of high dimensional QKD protocol against two realistic attack models, i.e. photon number splitting (PNS) attack and beam splitter (BS) attack. We present the high dimensional quantum key distribution system that incorporates a decoy-state scheme with complex structured light (OAM modes) using the KMB09 protocol. The complete QKD system design with experimental setup details and evaluation results are presented. The experimental results show that our proposed decoy-state scheme is robust against both PNS and BS attacks.
The security of conventional cryptography systems is threatened in the forthcoming era of quantum computers. Quantum key distribution (QKD) features fundamentally proven security and offers a promising option for quantum-proof cryptography solution. Although prototype QKD systems over optical fiber have been demonstrated over the years, the key generation rates remain several orders of magnitude lower than current classical communication systems. In an effort toward a commercially viable QKD system with improved key generation rates, we developed a discrete-variable QKD system based on time-bin quantum photonic states that can generate provably secure cryptographic keys at megabit-per-second rates over metropolitan distances. We use high-dimensional quantum states that transmit more than one secret bit per received photon, alleviating detector saturation effects in the superconducting nanowire single-photon detectors used in our system that feature very high detection efficiency (of more than 70%) and low timing jitter (of less than 40 ps). Our system is constructed using commercial off-the-shelf components, and the adopted protocol can be readily extended to free-space quantum channels. The security analysis adopted to distill the keys ensures that the demonstrated protocol is robust against coherent attacks, finite-size effects, and a broad class of experimental imperfections identified in our system.
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.