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.
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.
When built, quantum repeater networks will require classical network protocols to control the quantum operations. However, existing work on repeaters has focused on the quantum operations themselves, with less attention paid to the contents, semantics, ordering and reliability of the classical control messages. In this work we define and describe our implementation of the classical control protocols. The state machines and packet sequences for the three protocol layers are presented, and operation confirmed by running the protocols over simulations of the physical network. We also show that proper management of the resources in a bottleneck link allows the aggregate throughput of two end-to-end flows to substantially exceed that of a single flow. Our layered architectural framework will support independent evolution of the separate protocol layers. Networks of quantum repeaters utilize three concepts to execute a distributed algorithm that creates entangled quantum states between nodes that are far apart: a basic entanglement mechanism which depends on the physical implementation, error management (in this work, we study a method known as purification), and finally a quantum state propagation layer (here we implement entanglement swapping, which builds multi-hop connections from single-hop connections). Some researchers are investigating approaches that are substantially different from entanglement swapping [30, 24, 19]. Here we focus on swapping, but the layered architecture approach is broadly applicable, allowing other implementations to replace only a single layer in the protocol stack. Previous work primarily focused on the physical and mathematical tools for building repeaters. Classical information is also needed to enable teleportation and swapping, as many quantum operations are not deterministic, and results of quantum measurements need to be reported to distant partners before further operations can proceed. Also, operations in the middle of the network must be coordinated to route and swap properly. This requires classical messages to make operations robust, but message propagation times penalize performance. Even though this delay is usually included in repeater simulations, prior work has not defined the protocols in detail, especially with respect to how all of the nodes make consistent decisions in a timely fashion. In this work, we introduce a protocol stack for networks of quantum repeaters that considers all the necessary classical messages and which can be easily adapted for different approaches at all three protocol layers. We run simulations of competing flows on a dumbbell topology in order to increase our confidence in the behavior of our network protocols. By adjusting the fidelity thresholds required for entanglement swapping, we show that some configurations boost the aggregate throughput for multiple flows significantly above the maximum for a single flow, taking advantage of resources that would otherwise sit idle. The operation of such complex networks and such delicate tuning of the system without formal protocol definitions would not be possible. Previous work has also concentrated almost exclusively on the dedicated use of a single line or chain of repeaters, delivering Bell pairs only to the two nodes at the ends of the chain. Networks, however, typically have more than two end points, and allow any pair of these end nodes to communicate. More topologically complex networks, with numerous end nodes, are obviously much more scalable than connecting every possible pair of nodes using a dedicated line of repeaters. we investigate how classical multiplexing schemes translate to the domain of quantum repeaters, in order to manage shared resources and active communication flows of data from different stations. We simulate four sharing protocols in a complex network with competing traffic. Circuit switching gives any individual flow the best performance, but makes poor use of the overall network and is inflexible. We use circuit switching as our baseline case to compare time division multiplexing, buffer space multiplexing, and statistical multiplexing, and show that all multiplexing schemes are better than circuit switching. For the particular network simulated, we find that statistical multiplexing outperforms time division multiplexing by 28% and buffer space multiplexing by 13%. We find that all three multiplexing schemes are fair; each flow is penalized a similar percentage of its throughput as the the total number of users in the network increases. Finally, statistical multiplexing requires no network-wide coordination of the use of quantum memory or channels, and is easier to implement than a robust, scalable scheme for the other protocols. Our current results suggest that the best strategy for quantum repeater networks is statistical multiplexing. (This is in fact the quantum analogue of the basis on which the Internet works.) However, our current simulations are done with no degradation of memory over time, using the assumption of quantum error-corrected memory at each repeater; inclusion of decoherence and a finite qubit lifetime remains as future work.
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.
The reliable distribution of entanglement is essential for the effective operation of quantum networks. Due to fundamental differences between quantum and classical communication systems, it is necessary to develop specialised algorithms and protocols that also account for quantum-specific constraints. In this work, we focus on the issue of recalibration. As suggested by recent experimental studies, the process of local entanglement generation in a quantum link degrades over time due to environmental changes that have to be estimated and compensated via a fixed-duration calibration operation, during which the link is not available. Therefore, in such a quantum network, every link alternates between an activation period, during which it operates normally, and a calibration period, during which it cannot participate in the end-to-end entanglement distribution, thereby creating a trade-off between link quality (the initial fidelity of generated pairs, which decays during activation) and availability (the fraction of time the link is usable, which calibration reduces). We develop analytically a protocol for optimally assigning activation periods to each link in linear quantum repeater chains, subject to any general end-to-end fidelity requirements and local initial fidelity thresholds. Building on this foundation, we extend to general quantum networks, where multiple paths may cross at common links. To this, we propose a heuristic approach, evaluate it through simulations, and compare its performance with a benchmark, a numerical approach and theoretical bounds, confirming the analytical ordering of their performance.
Quantum communication enables a host of applications that cannot be achieved by classical communication means, with provably secure communication as one of the prime examples. The distance that quantum communication schemes can cover via direct communication is fundamentally limited by losses on the communication channel. By means of quantum repeaters, the reach of these schemes can be extended and chains of quantum repeaters could in principle cover arbitrarily long distances. In this work, we provide two efficient algorithms for determining the generation time and fidelity of the first generated entangled pair between the end nodes of a quantum repeater chain. The runtime of the algorithms increases polynomially with the number of segments of the chain, which improves upon the exponential runtime of existing algorithms. Our first algorithm is probabilistic and can analyze refined versions of repeater chain protocols which include intermediate entanglement distillation. Our second algorithm computes the waiting time distribution up to a pre-specified truncation time, has faster runtime than the first one and is moreover exact up to machine precision. Using our proof-of-principle implementation, we are able to analyze repeater chains of thousands of segments for some parameter regimes. The algorithms thus serve as useful tools for the analysis of large quantum repeater chain protocols and topologies of the future quantum internet.
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.
Quantum repeaters are an essential building block for realizing long-distance quantum communications. However, due to the fragile nature of quantum information, these repeaters suffer from loss and operational errors. Prior works have classified repeaters into three broad categories based on their use of probabilistic or near-deterministic methods to mitigate these errors. Besides differences in classical communication times, these approaches also vary in technological complexity, with near-deterministic methods requiring more advanced hardware. Recent increases in memory availability and advances in multiplexed entanglement generation motivate a fresh comparison of one-way and two-way repeater architectures. In this work, we present a two-way repeater protocol that combines multiplexing with application-aware distillation, designed for a setting where sufficient high-quality memory resources are available—reflecting architectural assumptions expected in large-scale network deployments. We introduce a recursive formulation to track the full probability distribution of Bell pairs in multiplexed two-way repeater architectures, enabling the performance analysis of multiplexed repeater schemes which use probabilistic n-to-k distillation. Using this framework, we compare the proposed two-way protocol with one-way schemes in parameter regimes previously believed to favour the latter, and find that the two-way architecture consistently outperforms one-way protocols while requiring lower technological and resource overheads. Quantum repeaters are a fundamental building block for long-distance quantum communication, yet they face challenges from loss and operational errors. The authors introduce a two-way repeater protocol leveraging multiplexing and application-aware distillation, demonstrating superior performance and reduced resource demands compared to one-way schemes, even in scenarios previously thought to favor the latter.