Abstract Efficient long-distance entanglement distribution is a key requirement for a global quantum internet. Quantum repeaters overcome photon loss in optical fibers, offering a route to long-distance entanglement distribution. Here, we study heralded quantum repeater architectures that are based on two-photon interference and integrate local or remote swapping. We derive an analytical expression for the entanglement distribution time as a function of transmission distance for both heralded local-swapping and remote-swapping schemes. This expression provides physical insight into how repeaters overcome channel loss in long-haul fibers. Considering a realistic quantum memory, we present theoretical curves showing the effect of finite memory lifetime on the entanglement distribution time. By comparing optimal distribution times over distances up to thousands of kilometers, we determine the optimal nesting architectures for the single-repeater channel in each scheme and compare the optimal distribution rates and entanglement fidelities of these schemes at various distances. Finally, by examining the limiting cases of zero channel loss, zero device loss, and lossless repeater systems, we find fundamental performance bounds for quantum repeaters. These results provide practical design principles for scalable quantum repeater networks and pave the way toward continent-scale quantum communication.
Abstract Efficient long-distance entanglement distribution is a key requirement for a global quantum internet. Quantum repeaters overcome photon loss in optical fibers, offering a route to long-distance entanglement distribution. Here, we study heralded quantum repeater architectures that are based on two-photon interference and integrate local or remote swapping. We derive an analytical expression for the entanglement distribution time as a function of transmission distance for both heralded local-swapping and remote-swapping schemes. This expression provides physical insight into how repeaters overcome channel loss in long-haul fibers. Considering a realistic quantum memory, we present theoretical curves showing the effect of finite memory lifetime on the entanglement distribution time. By comparing optimal distribution times over distances up to thousands of kilometers, we determine the optimal nesting architectures for the single-repeater channel in each scheme and compare the optimal distribution rates and entanglement fidelities of these schemes at various distances. Finally, by examining the limiting cases of zero channel loss, zero device loss, and lossless repeater systems, we find fundamental performance bounds for quantum repeaters. These results provide practical design principles for scalable quantum repeater networks and pave the way toward continent-scale quantum communication.
Long-distance transfer of quantum information is an essential ability for many applications of quantum science. A natural choice to distribute quantum information is to encode it into photons and transfer it through optical fibers. However, due to the unavoidable transmission losses present in every communication channel, the distances for efficient quantum communication via direct-state transfer are limited to a few hundred kilometers. To overcome this limitation, the use of quantum repeaters has been suggested. A quantum repeater protocol aims to establish entanglement (i.e., quantum correlation) between remote nodes by first generating entanglement over shorter distance pieces, storing it in quantum memories, and finally extending it to the whole distance using entanglement swapping. The main goal of this thesis is to design quantum repeater architectures using single solid-state quantum emitters and to develop the two-qubit gates required for performing entanglement swapping. We first explain the basic ideas of quantum repeaters and introduce potential material candidates, single erbium (168Er) and europium (151Eu) ions doped yttrium orthosilicate photonic crystals. Next, we propose a quantum repeater scheme combing erbium and europium ions to generate and distribute entanglement over long distances. We study the entanglement generation rate of the protocol and compare it with the rate of a well-known ensemble-based quantum repeater. Then, using cavity assisted interactions, we propose three different schemes to perform high fidelity two-qubit gates between single quantum systems. We quantify their expected performance in detail by taking into account many realistic imperfections and compare their strengths and weaknesses. The ability to perform local two-qubits gates is especially crucial in terms of distributing entanglement. Finally, based on our gained knowledge through these projects, we propose our second quantum repeater architecture based on erbium (167Er) ions, which outperforms the first scheme. We study two possibilities for distributing entanglement and calculate the overall fidelity as well as the distribution rate of the protocol.
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 networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information processing. Deterministic entanglement distribution over long distances is a prerequisite for scalable quantum networks, enabling the utilization of device-independent quantum key distribution (DI-QKD) and quantum teleportation to achieve secure and efficient information transfer. However, the exponential photon loss in optical fibres prohibits efficient and deterministic entanglement distribution. Quantum repeaters, incorporating entanglement swapping and entanglement purification with quantum memories, offer the most promising means to overcome this limitation in fibre-based quantum networks. Despite numerous pioneering efforts toward realizing quantum repeaters, a critical bottleneck remains, as remote memory-memory entanglement suffers from decoherence more rapidly than it can be established and purified over long distances. We overcome this by developing long-lived trapped-ion memories, an efficient telecom interface, and a high-visibility single-photon entanglement protocol. This allows us to establish and maintain memory-memory entanglement over a 10 km fibre within the average entanglement establishment time for the same distance. As a direct application, we demonstrate metropolitan-scale DI-QKD, distilling 1,917 secret keys out of 4.05*10^5 Bell pairs over 10 km. We further report a positive key rate over 101 km in the asymptotic limit, extending the achievable distance by more than two orders of magnitude. Our work provides a critical building block for quantum repeaters and marks an important step toward scalable quantum networks.
We present an exact rate analysis for a secret key that can be shared among two parties employing a linear quantum repeater chain. One of our main motivations is to address the question whether simply placing quantum memories along a quantum communication channel can be beneficial in a realistic setting. The underlying model assumes deterministic entanglement swapping of single-spin quantum memories and it excludes probabilistic entanglement distillation, and thus two-way classical communication, on higher nesting levels. Within this framework, we identify the essential properties of any optimal repeater scheme: entanglement distribution in parallel, entanglement swapping as soon and parallel quantum storage as little as possible. While these features are obvious or trivial for the simplest repeater with one middle station, for more stations they cannot always be combined. We propose an optimal scheme including channel loss and memory dephasing, proving its optimality for the case of two stations and conjecturing it for the general case. In an even more realistic setting, we consider additional tools and parameters such as memory cutoffs, multiplexing, initial state and swapping gate fidelities, and finite link coupling efficiencies in order to identify potential regimes in memory-assisted quantum key distribution beyond one middle station that exceed the rates of the smallest quantum repeaters as well as those obtainable in all-optical schemes unassisted by stationary memory qubits and two-way classical communication. Our analytical treatment enables us to determine simultaneous trade-offs between various parameters, their scaling, and their influence on the performance ordering among different types of protocols, comparing two-photon interference after dual-rail qubit transmission with one-photon interference of single-rail qubits or, similarly, optical interference of coherent states. We find that for experimental parameter values that are highly demanding but not impossible (up to 10 s coherence time, about 80% link coupling, and state or gate infidelities in the regime of 1%--2%), one secret bit can be shared per second at a total channel loss budget of 157.6 dB, i.e. a total distance of 800 km for a fiber attenuation length of 22 km with repeater stations placed at every 100 km---a clear improvement over realistic twin-field or, much more pronouncedly, ideal point-to-point quantum key distribution at GHz clock rates.
The realization of a global quantum network holds the potential to enable groundbreaking applications such as secure quantum communication and blind quantum computing. However, building such a network remains a formidable challenge, primarily due to photon loss in optical fibers. In this work, we propose a quantum repeater architecture for distributing entanglement over intercontinental distances by leveraging low-Earth-orbit satellites equipped with spontaneous parametric down-conversion (SPDC) photon-pair sources and ground stations utilizing single-atom memories in optical cavities and single-photon detectors to implement the cavity-assisted photon scattering (CAPS) gates for high-fidelity entanglement mapping. The efficient entanglement swapping is achieved by performing high-fidelity Rydberg gates and readouts. We evaluate the entanglement distribution rates and fidelities by analyzing several key imperfections, including time-dependent two-photon transmission and time-dependent pair fidelity, for various satellite heights and ground station distances. We also investigate the impact of pair source fidelity and spin decoherence rate on the repeater performance. Furthermore, we introduce a spatial-frequency multiplexing strategy within this architecture to enhance the design's performance. Finally, we discuss in detail the practical implementation of this architecture. Our results show that this architecture enables entanglement distribution over intercontinental distances. For example, it can distribute over 10000 pairs per flyby over 10000 km with a fidelity above 90%, surpassing the capabilities of terrestrial quantum repeaters
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.