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arXiv:2510.07471

Simulation of Quantum Repeater Networks under Decoherence and Purification Constraints

Wenhan Li, Shiyu Zhang

Published Oct 8, 2025• 0 citations
arXivHTMLPDF

Abstract

Long-distance quantum communication requires reliable entanglement distribution, but direct generation with protocols such as Barrett--Kok suffers from exponentially decreasing success probability with distance, making it impractical over hundreds of kilometers. Quantum repeaters address this by segmenting the channel and combining entanglement generation, swapping, and purification. In this work, we present a simulation framework for chain-based repeaters under continuous-time depolarizing noise. Our model implements heralded entanglement generation, Bell-state swapping, and multi-round purification, with configurable chain length, noise levels, and purification depth. Numerical results highlight how memory decoherence constrains performance, how purification mitigates fidelity loss, and how time and entanglement costs scale with distance. While simplified, the framework offers a flexible tool for exploring trade-offs in repeater design and provides a basis for extensions toward more complex network scenarios.

DOI
10.48550/arxiv.2510.07471

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Long-distance quantum communication requires reliable entanglement distribution, but direct generation with protocols such as Barrett--Kok suffers from exponentially decreasing success probability with distance, making it impractical over hundreds of kilometers. Quantum repeaters address this by segmenting the channel and combining entanglement generation, swapping, and purification. In this work, we present a simulation framework for chain-based repeaters under continuous-time depolarizing noise. Our model implements heralded entanglement generation, Bell-state swapping, and multi-round purification, with configurable chain length, noise levels, and purification depth. Numerical results highlight how memory decoherence constrains performance, how purification mitigates fidelity loss, and how time and entanglement costs scale with distance. While simplified, the framework offers a flexible tool for exploring trade-offs in repeater design and provides a basis for extensions toward more complex network scenarios.
First-generation quantum repeaters are essential in distributing entanglement over long distances since they could mitigate losses in optical fiber. Repeaters split the total distance into shorter, easier to generate links. Then, entanglement swapping establishes long range entanglement by performing local measurements at the repeaters and heralding their results. In this work, we develop an analytical model that estimates the impact of decoherence during heralding for a given protocol. Furthermore, we identify a competition between two phenomena: as repeater count increases, so does entanglement generation, but the additive impact of memory decoherence on final entanglement rate increases too. Therefore, we find that an optimal number of repeaters exists. These findings could lead the design of future quantum networks, both in the inter-repeater distance and swapping timings.
The distribution of high-quality entanglement over long distances remains a challenge due to losses in quantum channels. As a solution, quantum repeater protocols generate entanglement over short segments and progressively extend its range using entanglement swapping, while using distillation to compensate for entanglement degradation. Numerous studies analyze repeater protocols through tailored tools that are tied to specific protocol types and network assumptions. In this work, we propose a formal language to specify quantum repeater protocols in a unified manner, modeling the concurrent distribution of entanglement across multiple pairs of network nodes. We consider delays arising from failures and contention for resources, and account for the effects of noise and decoherence on the quality of entanglement. Furthermore, we provide a prototype tool based on our language to precisely track the rate and fidelity of the distributed entangled pairs, supporting heterogeneous hardware configurations and constraints on available quantum memories. Finally, we demonstrate the effectiveness of our approach by expressing common protocols from the literature and evaluating their performance.
We propose a purification-enhanced all-photonic quantum repeater scheme based on repeater graph states (RGS) framework that leverages the recently proposed half-RGS building block. This framework addresses a longstanding open question—how to naturally integrate entanglement purification with an all-photonic scheme—by enabling long-distance purification without disrupting the core design. Our framework utilizes optimistic purification performed directly on the half-RGS primitives across long distances without waiting for heralding outcomes. The overhead is modest: the RGS generation slows down proportionally with the number of purification rounds, and each round requires only one additional quantum emitter per half-RGS source. However, since the generation time is negligible compared to the end-to-end communication delay, the total latency remains effectively dominated by communication time, similar to frameworks without purification. Our framework enables flexible purification scheduling along the connection path, making it compatible with memory-based strategies, a rich body of research on purification scheduling and optimization that was previously thought inapplicable to the RGS scheme. Through numerical evaluation, we compare the performance of our framework with purification between memories at end nodes.
Quantum repeater networks that allow long-distance entanglement distribution will be the backbone of distributed quantum information processing. In this paper we explore entanglement distribution using quantum repeaters with optimized buffer time, equipped with noisy quantum memories and performing imperfect entanglement purification and swapping. We observe that increasing the number of memories on end nodes leads to a higher entanglement distribution rate per memory and higher probability of high-fidelity entanglement distribution, at least for the case with perfect operations. When imperfect operations are considered, however, we make the surprising observation that the permemory entanglement rate decreases with increasing number of memories. Our results suggest that building quantum repeaters that perform well under realistic conditions requires careful modeling and design that takes into consideration the operations and resources that are finite and imperfect.
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
Quantum communication is a groundbreaking technology that is driving the future of information transmission and communication technologies to a new paradigm. It relies on quantum entanglement to facilitate the transmission of quantum states between parties. Quantum repeaters are crucial for facilitating long-distance quantum communication. These quantum devices act as intermediaries between adjacent communication channel segments within a fragmented quantum network, allowing for entanglement swapping between the channel segments. This entanglement swapping process establishes entanglement links between the endpoints of adjacent segments, gradually creating a continuous entanglement connection over the entire length of the transmission channel. The established quantum link can be utilized for secure and efficient quantum communication between distant sender and receiver nodes. This study focuses on quantum entanglement purification, a protocol aimed at maintaining high fidelity entangled states above the operational threshold of the communication channel. This study investigates the optimal stage for executing the purification protocol and applies optimization schemes to evaluate various purification protocols. We use IBM Qiskit for circuit implementation and simulation. The results offer valuable insights into future approaches to implementing practical quantum repeaters and shed light on existing and anticipated challenges.