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arXiv:2405.04207 · Quantum

On High-Dimensional Twin-Field Quantum Key Distribution

Ronny Müller, Mujtaba Zahidy, Leif Katsuo Oxenløwe, Søren O. Forchhammer, Davide Bacco

Published Oct 1, 2025• 0 citations
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Abstract

Twin-Field Quantum Key Distribution (QKD) is a QKD protocol that uses single-photon interference to perform QKD over long distances. QKD protocols that encode information using high-dimensional quantum states can benefit from increased key rates and higher noise resilience. We define the essence of Twin-Field QKD and explore its generalization to higher dimensions. Further, we show that, ultimately, the Twin-Field protocol cannot be generalized to higher dimensions in accordance with our definition.

DOI
10.22331/q-2025-10-01-1869

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Twin-Field Quantum Key Distribution (QKD) is a QKD protocol that uses single-photon interference to perform QKD over long distances. QKD protocols that encode information using high-dimensional quantum states can benefit from increased key rates and higher noise resilience. We define the essence of Twin-Field QKD and explore its generalization to higher dimensions. Further, we show that, ultimately, the Twin-Field protocol cannot be generalized to higher dimensions in accordance with our definition.
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Twin field quantum key distribution (TF-QKD) has attracted the attention of the research community thanks to its higher secure key rate which scales as square root of the channel transmittance. The twin field secure key rate thus crosses the repeaterless secure key rate distance bound, showing that the protocol can cater to large channel lengths. Here, we present a twin-field-like QKD protocol based on single photon interference of differential phase shift (DPS) encoded states and prove the security of the scheme. Our protocol builds upon an existing measurement device independent (MDI) QKD system that has a DPS encoding and modifies the sifting step to one based on single photon interference. We demonstrate security of our DPS-twin-field (DPS-TF) protocol against collective attacks and quantify the secure key rate. We find that with the current state-of-the-art technology, both TF-QKD and MDI-QKD protocols with the DPS encoding work almost identically in terms of the channel length, although the achievable secure key rate of the DPS-TF QKD is higher compared to MDI-QKD.
The twin-field quantum key distribution (TF-QKD) protocol has led to extensive investigation for its capacity of overcoming the rate-distance limit. One variant for TF-QKD named sending-or-not-sending (SNS) TF-QKD has also been proposed. The SNS-TF-QKD encodes the classical keys 0 and 1 in sending or not sending the phase-randomized coherent states, which helps it to tolerate large misalignment errors due to optical phase fluctuations. Nevertheless, the original SNS-TF-QKD scheme utilizes only single-photon interference in generating secret keys, which seems quite different from other TF-QKD protocols. In this paper, we prove that multiphoton interference in the SNS TF-QKD protocol can also contribute to key generation. Accordingly, an improved SNS-TF-QKD scheme with higher key rate is proposed, where events of not only single-photon but also two-photon emissions are considered as effective events.
Quantum Key Distribution (QKD) offers information-theoretic security, making it a cornerstone of future cryptographic infrastructures in the era of quantum computing. However, long-distance deployment of conventional QKD protocols is limited by channel losses, detector noise, and the fundamental repeaterless Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound. To address these challenges, this paper investigates the Twin-Field QKD (TF-QKD) protocol, which enables secure key exchange over long-haul optical fibers by exploiting single-photon interference at an untrusted intermediate node. An elaborate system model is provided with optical channel impairments, imperfections of detector and phase stabilization conditions. Finite-key analysis, error correction as well as privacy amplification are placed and made together in order to increase robustness of protocol against practical attacks. The simulation data show that TFQKD can reach secure key rates of over 500 km and is out of reach of decoy-state QKD but nearly close to fundamental limits. These results demonstrate that TF-QKD has the potential to practicalize quantumsecure communication at large scale and in a costeffective way, which can constitute a sub-unit of the future quantum internet.
Abstract Quantum key distribution (QKD) offers a reliable solution to communication problems that require long-term data security. For its widespread use, however, the rate and reach of QKD systems must be improved. Twin-field (TF) QKD is a step forward toward this direction, with early demonstrations suggesting it can beat the current rate-versus-distance records. A recently introduced variant of TF-QKD is particularly suited for experimental implementation, and has been shown to offer a higher key rate than other variants in the asymptotic regime, where users exchange an infinite number of signals. Here, we extend the security of this protocol to the finite-key regime, showing that it can overcome the fundamental bounds on point-to-point QKD with ~1010 transmitted signals. In many practical regimes of interest, our analysis offers higher key rates than those of alternative variants. Moreover, some of the techniques we develop are applicable to the finite-key analysis of other QKD protocols.