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arXiv:2507.04322 · Physical Review Research

High-rate qutrit entanglement swapping with photon-number basis

Kazufumi Tanji, Hikaru Shimizu, Masahiro Takeoka

Published Feb 23, 2026• 1 citation
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Abstract

Entanglement generation between distant nodes is a fundamental process in distributed quantum information processing. Qudits, high-dimensional quantum states, are promising candidates for enhancing entanglement distribution capabilities. However, the success probability of qudit entanglement distribution using Bell measurements is typically lower than that of conventional qubit-based protocols. In this paper, we propose an entanglement swapping protocol specifically designed for qutrits (three-dimensional quantum states). Our protocol employs photon-number encoding combined with an additional mode basis, such as polarization, effectively increasing the success probability. We show that the proposed qutrit protocol can achieve higher entanglement generation rates compared to conventional two-photon detection-based qubit protocols, especially under conditions of limited photon generation probability. Furthermore, we evaluate our protocol under realistic experimental imperfections, including photon loss and threshold detection, and show that it achieves high fidelity with probabilistic photon sources.

DOI
10.1103/gx4k-y5gf

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Entanglement generation between distant nodes is a fundamental process in distributed quantum information processing. Qudits, high-dimensional quantum states, are promising candidates for enhancing entanglement distribution capabilities. However, the success probability of qudit entanglement distribution using Bell measurements is typically lower than that of conventional qubit-based protocols. In this paper, we propose an entanglement swapping protocol specifically designed for qutrits (three-dimensional quantum states). Our protocol employs photon-number encoding combined with an additional mode basis, such as polarization, effectively increasing the success probability. We show that the proposed qutrit protocol can achieve higher entanglement generation rates compared to conventional two-photon detection-based qubit protocols, especially under conditions of limited photon generation probability. Furthermore, we evaluate our protocol under realistic experimental imperfections, including photon loss and threshold detection, and show that it achieves high fidelity with probabilistic photon sources.
Polarization entanglement is widely used in optical quantum information processing as well as quantum communication due to its compatibility with standard optical components. However, distributing polarization entanglement is severely limited by photon loss in the channels. In conventional methods, the distribution rate of polarization entanglement scales linearly with the end-to-end channel transmittance, which decreases exponentially with distance. Here, we propose and experimentally demonstrate a protocol for distributing polarization entanglement with improved rate-loss scaling. The protocol combines single-click entanglement swapping with polarization–photon-number hybrid entanglement, in which the photon-number-basis modes are sent to a central swapping node while the polarization qubits are retained by the end users. In our experiment, we observed a square-root improvement in the rate-loss scaling compared with conventional methods and achieved a fidelity of 0.843 for distributed polarization-entangled photon pairs. These results provide a proof-of-principle demonstration that the favorable rate-loss scaling of single-click entanglement swapping can be transferred to polarization entanglement distribution.
Entanglement between distant parties is a key resource in quantum networks. However, photon losses in quantum channels significantly reduce the success probability of entanglement sharing, which scales quadratically with the channel transmittivity. Quantum repeaters using entanglement swapping can mitigate this effect, but usually require high-performance photonic quantum memories to synchronize photonic qubits. In this work, we theoretically and experimentally investigate an entanglement swapping protocol using photon-number-encoded states that can effectively alleviate quantum channel losses without requiring photonic quantum memories. We demonstrate that the protocol exhibits a success probability scaling linearly with the channel transmittivity. Furthermore, we show that while unbalanced channel losses can degrade the shared entanglement, this effect can be compensated by optimally adjusting the initial entangled states. Our results highlight the potential of photon-number encoding for realizing robust entanglement distribution in lossy quantum networks.
Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pairs, which can significantly reduce the required coherence time of the qubit registers. However, current schemes require fast optical switching, which is experimentally challenging. In addition, the higher degree of error correlation between the generated entangled pairs in qudit protocols compared to qubit protocols has not been widely studied in detail. We propose a qudit-mediated entangling protocol that completely circumvents the need for optical switches at the expense of a lower success probability of the scheme. Furthermore, we quantify the amount of error correlation between the simultaneously generated entangled pairs and analyze the effect on entanglement purification algorithms and teleportation-based quantum error correction. We find that optimized purification schemes can efficiently correct the correlated errors, while the quantum error correction codes studied here perform worse than for uncorrelated error models. Published by the American Physical Society 2024
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell- state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful, we explore the theoretical possibilities of realizing unit-fidelity quantum teleportation and entanglement swapping with 2525%25 success probability. This photon-assisted Bell projection is generated by coupling almost resonantly the two material qubits to single modes of the radiation field in two separate cavities in a Ramsey-type interaction sequence and by measuring the emerged field states in a balanced homodyne detection scenario. As these quantum protocols require basic tools of quantum state engineering of coherent multiphoton states and balanced homodyne photodetection, they may offer interesting perspectives in particular for current quantum optical applications in 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.
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.