Memory-based Quantum Repeaters Enable Long-Distance Communication with Single Photons Every 50-100km

Long-distance quantum communication represents a significant challenge, demanding methods that overcome the limitations of transmitting fragile quantum information over vast distances. Stefan Häussler, Peter van Loock, and colleagues at Johannes Gutenberg-Universität Mainz now demonstrate a promising approach, developing an all-optical quantum repeater that relies on storing quantum information in fibre loops and employing error-correcting codes. This innovative system achieves long-distance communication by sending single photons between repeater stations, operating efficiently within the existing infrastructure used for classical communication. The research establishes a pathway towards scalable quantum networks, successfully modelling communication across distances up to 10,000 kilometres and offering a practical alternative to complex entanglement-sharing protocols.

Similar intervals exist, however, existing all-optical quantum communication protocols either require complicated quantum error correction steps for logical-qubit recoveries at every few kilometers or, over larger quantum repeater segments, they depend on sharing complex multi-photon entangled states. This work proposes an all-optical memory-based quantum repeater for long-distance quantum communication, with quantum memories at each repeater station realised in the form of fiber loops combined with suitable quantum error correction codes for photon-loss protection. By sending only single-photon states through the fibers connecting the stations, such repeaters can operate in the classical regime.

All-Optical Quantum Repeater with Error Correction

The research team developed an all-optical memory-based repeater system for long-distance quantum communication, designed to operate effectively within the infrastructure of existing classical fiber networks. This system utilizes fiber loops at each repeater station to create quantum memories, coupled with error-correcting codes to protect against photon loss during transmission. By transmitting single-photon states, the repeater avoids the complexities of multi-photon entanglement required by other all-optical protocols, enabling operation over extended distances. The performance of this scheme was analyzed using the Gottesman-Kitaev-Preskill code, combined with the Steane code, and the single-photon parity code, with simulations extending to total distances of up to 10000km.

A key innovation lies in the method for correcting Gaussian shifts in the quantum data, arising from imperfections in the system. The team devised a technique to estimate these shifts by mapping them onto a representative value within a defined range, allowing for accurate correction when the shift is sufficiently small. However, larger shifts introduce errors, specifically Pauli-X errors, which are carefully modeled and accounted for in the overall system performance. The probability of these Pauli errors, both during intermediate correction steps and during entanglement swapping, is calculated using complex integrals and circular convolution, allowing for precise prediction of the quantum bit error rate.

To further refine the accuracy of the model, the researchers incorporated the potential for Pauli errors originating from the generation of entangled states, quantifying these errors with a probability related to the squeezing variance of the GKP modes used in state preparation. This probability is then integrated into the overall error rate calculation, accounting for the total number of potential errors introduced during state generation and correction. The team developed a Steane transfer function to map errors onto the qubit level, allowing for a comprehensive assessment of the system’s performance under realistic conditions. This detailed modeling approach enables accurate prediction of the error rate and optimization of the repeater system for long-distance quantum communication.

Optimal Quantum Repeater Parameters for Communication

The research presents a rigorous mathematical analysis of quantum repeater schemes for long-distance quantum communication, aiming to determine the optimal parameters to maximize the rate at which secure keys can be established. The analysis considers various sources of noise and error, including state preparation errors, channel loss, and imperfect measurements. The study identifies two complementary operational regimes: fewer resource states with a higher number of repeater stations, suitable when state generation is costly, and more intermediate correction steps with fewer stations, suitable when repeater stations are costly. The researchers characterized the statistical properties of the waiting times between entanglement distribution events, crucial for understanding the overall performance of the repeater.

They provide a detailed mathematical analysis of these waiting times, including the probability distribution and expectation value. The analysis suggests that the optimal encoding scheme depends on the specific application and the characteristics of the communication channel. The document includes mathematical derivations, including the probability distribution of the absolute value of the difference between two geometric random variables and the expectation value of the exponential of the summed waiting time.

All-Optical Quantum Repeaters Enable Long-Distance Communication

This research presents a novel approach to quantum repeaters, devices essential for extending the range of quantum communication. The team has developed an all-optical system that utilizes fiber loops to store and correct quantum information, encoded using established quantum error correction codes. Unlike many existing proposals, this scheme transmits only single photons through standard optical fibers, making it compatible with existing telecommunications infrastructure. Through analysis of the Gottesman-Kitaev-Preskill code, alongside concatenations with the Steane code and the single-photon parity code, the researchers demonstrate the potential for reliable quantum communication over distances up to 10,000 kilometers.

The achieved performance, with raw rates of 3.5Hz at 1000km and approximately 2Hz at 10,000km, indicates a viable path towards long-distance quantum networks. While acknowledging that these rates may benefit from multiplexing techniques, the study confirms the feasibility of operating with long segments, mirroring the capabilities of classical optical communication. The team highlights the advantage of avoiding complex multi-photon entanglement, simplifying the practical implementation of the system. Future work may focus on optimizing multiplexing strategies and further enhancing the quality of resource states to improve communication rates and extend the reach of quantum networks.