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arXiv:2502.04450 · npj Quantum Information

Merging-based quantum repeater

Maria Flors Mor-Ruiz, Jorge Miguel-Ramiro, Julius Wallnöfer, Tim J. Coopmans, Wolfgang Dür

Published Aug 5, 2026• 0 citations
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Abstract

Abstract We introduce a merging-based quantum repeater that departs from the conventional swapping paradigm by progressively growing multipartite entanglement. In contrast to swapping-based schemes, where a single failed operation often forces the entire protocol to restart, our approach reuses previously established entanglement through iterative gap-patching, thereby reducing waiting times, improving distribution rates, and introducing enhanced flexibility in the communication requests. We analyze this protocol in the context of probabilistic operations and a time-dependent dephasing noise model. We compare it with standard repeater protocols and demonstrate a clear advantage in secret-key rate across relevant operating regimes, underscoring its potential for practical quantum communication scenarios. These results establish merging-based repeaters as a promising alternative design principle for scalable and resource-efficient quantum-network architectures.

DOI
10.1038/s41534-026-01340-w

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Abstract We introduce a merging-based quantum repeater that departs from the conventional swapping paradigm by progressively growing multipartite entanglement. In contrast to swapping-based schemes, where a single failed operation often forces the entire protocol to restart, our approach reuses previously established entanglement through iterative gap-patching, thereby reducing waiting times, improving distribution rates, and introducing enhanced flexibility in the communication requests. We analyze this protocol in the context of probabilistic operations and a time-dependent dephasing noise model. We compare it with standard repeater protocols and demonstrate a clear advantage in secret-key rate across relevant operating regimes, underscoring its potential for practical quantum communication scenarios. These results establish merging-based repeaters as a promising alternative design principle for scalable and resource-efficient quantum-network architectures.
We present a quantum repeater protocol for distributing entanglement over long distances, where a dedicated communication stage enables trial rates not limited by the travel time between repeater nodes. To accomplish this, each node contains several qubits that can couple to one single-photon emitter. Photons from the emitters in neighboring nodes generate heralded entanglement between qubits in these nodes. The protocol leaves the emitters disentangled from the rest of the system immediately after emitting the photons, thus allowing them to be reused to entangle other qubits without waiting for the repeater link round-trip time. This time multiplexing increases the protocol trial rate by up to an order of magnitude. The protocol is then combined with conventional deterministic entanglement swapping and heralded entanglement purification to extend the entanglement distance and reduce the entanglement error, respectively. We perform a complete protocol analysis by considering all relevant error sources, such as initialization, two-qubit gate, and qubit measurement errors, as well as the exponential decoherence of the qubits with time. The latter is particularly important since we analyze the protocol performance for a broad range of experimental parameters and obtain secret key rates ranging from 1 to 1000 Hz at a distance of 1000 km. Our results suggest that it is important to reach a qubit memory coherence time of around 1 s, and two-qubit gate and measurement errors on the order of 10 − 3 to obtain reasonable secret key rates over distances longer than achievable with direct transmission. While this work focuses on optimizing secret key rates, the protocol can also be used for Einstein-Podolsky-Rosen pair generation and is thus also relevant for, e.g., distributed quantum computing.
The standard approach to realize a quantum repeater relies upon probabilistic but heralded entangled state manipulations and the storage of quantum states while waiting for successful events. In the literature on this class of repeaters, calculating repeater rates has typically depended on approximations assuming sufficiently small probabilities. Here we propose an exact and systematic approach including an algorithm based on Markov chain theory to compute the average waiting time (and hence the transmission rates) of quantum repeaters with arbitrary numbers of links. For up to four repeater segments, we explicitly give the exact rate formulas for arbitrary entanglement swapping probabilities. Starting with three segments, we explore schemes with arbitrary (not only doubling) and dynamical (not only predetermined) connections. The effect of finite memory times is also considered and the relative influence of the classical communication (of heralded signals) is shown to grow significantly for larger probabilities. Conversely, we demonstrate that for small swapping probabilities the statistical behavior of the waiting time in a quantum repeater cannot be characterized by its average value alone and additional statistical quantifiers are needed. For large repeater systems, we propose a recursive approach based on exactly but still efficiently computable waiting times of sufficiently small subrepeaters. This approach leads to better lower bounds on repeater rates compared to existing schemes.
All-photonic quantum repeaters are essential for establishing long-range quantum entanglement. Within repeater nodes, reliably performing entanglement swapping is a key component of scalable quantum communication. To tackle the challenge of probabilistic Bell state measurement in linear optics, which often leads to information loss, various approaches have been proposed to ensure the loss tolerance of distributing a single ebit. We have generalized previous work regarding repeater graph states with elaborate connectivity, enabling the efficient establishment of exploitable ebits at a finite rate with high probability. We demonstrate that our new scheme significantly outperforms the previous work with much flexibility and discuss the generation overhead of such resource states. These findings offer new insights into the scalability and reliability of loss-tolerant quantum networks.
We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeaters' sizes. Based on this, we are able to demonstrate that the commonly used "doubling" scheme for performing probabilistic entanglement swapping of probabilistically distributed entangled qubit pairs in quantum repeaters does not always produce the best possible raw rate. Focusing on this figure of merit, without considering additional probabilistic elements for error suppression such as entanglement distillation on higher "nesting levels," our approach reveals that a power-of-two number of segments has no privileged position in quantum repeater theory; the best scheme can be constructed for any number of segments. Moreover, classical communication can be included into our scheme, and we show how this influences the raw waiting time for different numbers of segments, confirming again the optimality of "nondoubling" in some relevant parameter regimes. Thus, our approach provides the minimal possible waiting time of quantum repeaters in a fairly general physical setting.
Quantum communication enables the implementation of tasks that are unachievable with classical resources. However, losses on the communication channel preclude the direct long-distance transmission of quantum information in many relevant scenarios. In principle, quantum repeaters allow one to overcome losses. However, realistic hardware parameters make long-distance quantum communication a challenge in practice. For instance, in many protocols an entangled pair is generated that needs to wait in quantum memory until the generation of an additional pair. During this waiting time the first pair decoheres, impacting the quality of the final entanglement produced. At the cost of a lower rate, this effect can be mitigated by imposing a cutoff condition. For instance, a maximum storage time for entanglement after which it is discarded. In this article, we optimize the cutoffs for quantum repeater chains. First, we develop an algorithm for computing the probability distribution of the waiting time and fidelity of entanglement produced by repeater chain protocols which include a cutoff. Then, we use the algorithm to optimize cutoffs in order to maximize the secret-key rate between the end nodes of the repeater chain. In this article, we find that the use of the optimal cutoff extends the parameter regime for which secret key can be generated and, moreover, significantly increases the secret-key rate for a large range of parameters.
We propose a repeat-until-success protocol to improve the performance of probabilistic quantum repeaters. Conventionally, these rely on passive static linear-optics elements and photodetectors to perform Bell-state measurements (BSMs) with a maximum success rate of 50%. This is a strong impediment for entanglement swapping between distant quantum memories. Every time a BSM fails, entanglement needs to be redistributed between the corresponding memories in the repeater link. The key ingredients of our scheme are repeatable BSMs. Under ideal conditions, these turn probabilistic quantum repeaters into deterministic ones. Under realistic conditions, our protocol too might fail. However, using additional threshold detectors now allows us to improve the entanglement generation rate by almost orders of magnitude, at a nominal distance of 1000 km, compared to schemes that rely on conventional BSMs. This improvement is sufficient to make the performance of our scheme comparable to the expected performance of some deterministic quantum repeaters.