Extending Quantum Links: Modules for Fiber‐ and Memory‐Based Quantum Repeaters
Peter van Loock, Wolfgang Alt, Christoph Becher, Oliver J. Benson, Holger Boche, Christian Deppe, Jürgen Eschner, Sven Höfling, Dieter Meschede, Peter Michler, Frank Schmidt, Harald Weinfurter
Abstract Elementary building blocks for quantum repeaters based on fiber channels and memory stations are analyzed. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. The performances of basic quantum repeater links for these platforms are evaluated and compared, both for present‐day, state‐of‐the‐art experimental parameters as well as for parameters that can in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances—up to a few 100 km—in which the repeater‐assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. Two different protocols are considered, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, nondestructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.
Abstract Elementary building blocks for quantum repeaters based on fiber channels and memory stations are analyzed. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. The performances of basic quantum repeater links for these platforms are evaluated and compared, both for present‐day, state‐of‐the‐art experimental parameters as well as for parameters that can in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances—up to a few 100 km—in which the repeater‐assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. Two different protocols are considered, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, nondestructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.
We propose and analyze a hybrid quantum repeater architecture that combines two leading hardware platforms: quantum dots (QDs) as bright, deterministic sources of entangled photon pairs and group-IV-vacancy centers in diamond as efficient, heralded quantum memories. This combination leverages high-rate entanglement generation together with long-lived storage, enabling scalable entanglement distribution over long distances. A key challenge is the large bandwidth mismatch between QD photons and the narrow optical transitions of the memories. We combine a comprehensive model of the spin-photon interface, including full spin-photon coupling dynamics, and explore mitigation strategies such as frequency filtering and optimized magnetic-field orientation. Our results show that with optimized designs, photon-to-memory transfer can be achieved with high efficiency and fidelity, supporting the feasibility of such hybrid systems. Finally, we analyze a full repeater chain using experimentally achievable parameters and find that a network with thousands of memories across several repeater nodes could achieve a secret-key rate of 500 bit/s over 1,000 km, demonstrating the strong potential of this approach for next-generation quantum networks.
This thesis is an exploration of quantum repeaters from a practical point of view. Quantum repeaters are devices which help improve the quantum communication capacity of a lossy bosonic channel (which include photonic channels such as optical fiber) beyond what is possible using a purely lossy channel. The analyses in this thesis involve modeling the experimental imperfections inherent in the various devices which comprise a quantum repeater, then combining these models to calculate various quantities of interest. \n \nTwo systems are analyzed in this thesis. One is a simple quantum repeater, while the other is a potential building block for more complex quantum repeaters. \n \nThe simple quantum repeater scheme can be implemented with currently available technology. In it, two parties perform quantum key distribution (QKD) by exchanging photons with two quantum memories placed between them. Its secret key rate ideally scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account imperfections in the setup, such as detector efficiency and dark counts, we present parameter regimes in which our protocol outperforms protocols based on direct transmission. We find that implementing our scheme with trapped ions is a promising way to reach the necessary parameter regimes, and that the regimes are easier to reach if the optical channels are very lossy. \n \nThe creation of entanglement between two quantum memories is an important building block in some quantum repeater schemes. We consider a specific quantum memory consisting of an atom trapped in a cavity. The system allows a CNOT operation to be performed between an atom and a photon. We study three methods for taking advantage of this to entangle two atoms: (1) interacting a coherent pulse with each atom, then performing an entangling measurement on the pulses; (2) interacting a single coherent pulse with each atom sequentially; (3) emitting an entangled photon from one atom and interacting it with the other atom. The success probability of each method is compared, as well as the quality of the entangled states produced by each one, taking into account imperfections which appear in a specific experimental implementation of such memories. We find that there is a tradeoff between success probability and entangled state quality when coherent states are used, and that method 3 provides higher-quality entangled states than is possible with the other two methods.
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.
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.
An overview will be given of various approaches to implementing a quantum repeater for quantum communication over large distances. This includes a discussion of systems and protocols that are experimentally feasible and thus realizable in the midterm in order to go beyond the current limit of a few hundred km given by direct quantum-state transmissions. At the same time, these schemes should be, in principle, scalable to arbitrary distances. In this context, the influence of various elements and strategies in a quantum repeater protocol on the final fidelities and rates shall be addressed: initial entanglement distribution, Bell measurements, multiplexing, postselection, quantum memories, and quantum error detection/correction. Solely on the hardware side, the differences in using just single quanta or instead employing many quanta for the flying (photons) and the stationary (atoms) qubits will be pointed out.
Future quantum networks will enable the realisation of a large family of quantum protocols, hence allowing for implementation of various tasks ranging from quantum cryptography through quantum computing to quantum metrology.In this thesis we analyse and develop the building blocks of quantum repeater networks.These networks consist of quantum repeater nodes, which are equipped with quantum memories enabling storage of quantum information.The repeater nodes are connected using optical fibres that enable for the transmission of photonic quantum signals between the repeater nodes.We specifically focus on the two building blocks: remote entanglement generation and entanglement distillation.We then investigate various proof of principle quantum repeater schemes used for generating shared secret key between distant parties.The repeater schemes that we consider utilise one to three memory nodes capable of generating memory-photon entanglement.Finally, we introduce a novel framework for investigating a foundational aspect in the use of quantum communication related to the uncertainty principle.Efficient remote entanglement generation is an indispensable building block of most near-term quantum repeater networks.In this thesis we consider various remote entanglement generation schemes that permit multiplexing, which aims at increasing the throughput of this procedure.We find that for the specific schemes that are suitable for platforms with a single communication qubit and multiple memory qubits, the performance of the multiplexing approach is strongly dependent on the time it takes to perform local operations within the memory nodes.Entanglement distillation enables for filtering out the noise from imperfect entangled states using only local operations and classical communication.Using a general framework for optimising such schemes, which we have developed, we have proven optimality of specific generic and experimentally relevant distillation schemes.We have developed a general framework for optimising such schemes, which we have used to prove optimality of various generic and experimentally relevant distillation schemes.In designing proof of principle quantum repeater schemes we assume an informationtheoretic approach, which enables us to assess their performance in a hardware-agnostic way.We find that all the schemes that we consider can prove useful in specific parameter regimes for the nitrogen-vacancy centre platform.Moreover, we find that one scheme which has already been realised experimentally in the context of remote entanglement generation, is expected to significantly outperform every possible system based on direct communication without repeaters.However, our analysis shows that encapsulating the nitrogen-vacancy centres in optical cavities for the enhancement of the emission rates is a necessary requirement for such a successful demonstration of the first proofof-principle quantum repeater.xi xii SUMMARY Finally, we investigate the quantum uncertainty principle which is a fundamental feature of quantum mechanics, allowing for security in many quantum cryptographic protocols.We find that in a particular scenario, relevant from the perspective of quantum key distribution, a significant part of the observed uncertainty is in fact due to lack of information rather than intrinsic.If the eavesdropper could access that information, she would be able to much better, or in some cases even with certainty, guess the value of the raw bit of the generated key.