Reliable Quantum Links: Entanglement, Error Correction, and Classical Communication
Mahmoud Saad Abouamer, Jaemin Kim, Jaron Skovsted Gundersen, René Bødker Christensen, Jakob Kaltoft Søndergaard, Søren Pilegaard Rasmussen, Jan Østergaard, Petar Popovski
This paper is a tutorial-style introduction to methods and protocols for reliable transmission of quantum information over noisy quantum links. The exposition is based on a design philosophy that parallels classical link-layer mechanisms such as forward error correction and Automatic Repeat reQuest (ARQ). It starts by drawing analogies and highlights differences between classical and quantum links. Such analogies are used as guiding principles, with explicit attention to where the classical correspondence no longer applies and where non-classical constraints and resources govern the protocol design. The emphasis is on the fact that classical reliability is achieved through fungible and cloneable bits, whereas unknown quantum states cannot be copied or freely retransmitted. In addition, quantum information is subject to stringent physical constraints due to decoherence as well as the need for transduction between stationary and flying qubits. Quantum error correction is presented as the analogue of classical forward error correction, where logical qubits are protected by encoding them into larger entangled code spaces and using syndrome measurements to infer and correct errors without collapsing the encoded state. It then introduces teleportation-based link abstractions, in which transmission of an unknown qubit is realized by consuming shared Bell pairs together with classical messages. Entanglement purification protocols play a role similar to ARQ-style reliability enhancement by converting many noisy entangled pairs into fewer, higher-fidelity pairs at the cost of additional resources. The paper is written from the perspective of classical communication engineering and is intended as a guide for translating the relevant ideas toward reliable quantum links and networks.
This paper is a tutorial-style introduction to methods and protocols for reliable transmission of quantum information over noisy quantum links. The exposition is based on a design philosophy that parallels classical link-layer mechanisms such as forward error correction and Automatic Repeat reQuest (ARQ). It starts by drawing analogies and highlights differences between classical and quantum links. Such analogies are used as guiding principles, with explicit attention to where the classical correspondence no longer applies and where non-classical constraints and resources govern the protocol design. The emphasis is on the fact that classical reliability is achieved through fungible and cloneable bits, whereas unknown quantum states cannot be copied or freely retransmitted. In addition, quantum information is subject to stringent physical constraints due to decoherence as well as the need for transduction between stationary and flying qubits. Quantum error correction is presented as the analogue of classical forward error correction, where logical qubits are protected by encoding them into larger entangled code spaces and using syndrome measurements to infer and correct errors without collapsing the encoded state. It then introduces teleportation-based link abstractions, in which transmission of an unknown qubit is realized by consuming shared Bell pairs together with classical messages. Entanglement purification protocols play a role similar to ARQ-style reliability enhancement by converting many noisy entangled pairs into fewer, higher-fidelity pairs at the cost of additional resources. The paper is written from the perspective of classical communication engineering and is intended as a guide for translating the relevant ideas toward reliable quantum links and networks.
The quantum internet, which will be a hybrid of quantum and classical networks, is expected to provide information-theoretic security for data transmission. Classical networks have well-established protocols for reliable end-to-end transmission that use duplicating the classical bits implicitly. However, due to the no-cloning theorem, quantum bits (qubits) cannot be copied. In this paper, we propose to use a Universal Quantum Copying Machine (UQCM) to create imperfect clones and summarizes the Quantum Automatic Repeat Request (QARQ) protocol, which is inspired by its classical counterpart. To investigate the viability of QARQ, a simulation platform is created considering Nitrogen-vacancy (NV) center qubit platform that implements QARQ for quantum communication. The results explore the applications it is suitable for while maintaining enough quality of the qubit state. Two major quantum technologies are studied for these protocols: Direct Transmission (DT), and Teleportation (TP). It has been shown that for short distance communication DT provides better fidelity than TP while for long-distance communication TP outperforms DT and hence improves the QARQ performance as well.
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.
Today's communications networks are filled with Web pages, e-mails, telephone conversations, video clips, financial transactions, and more, all encoded digitally as bursts of light flashing through fiber-optic cables. All of these messages can be boiled down to sequences of bits, 0's and 1's—usually long sequences, measured in kilobits, megabits, or sometimes even gigabits. But light, like everything else, behaves according to the laws of quantum mechanics, and a sequence of bits is not a good way to describe the properties of a quantum object. Instead, we should turn to quantum bits, or “qubits,” and someday, perhaps, today's network traffic will be supplemented by streams of such quantum information. Quantum transmissions would enable cryptographic systems to detect attempted eavesdropping, and quantum computers capable of manipulating quantum information could solve some problems far more rapidly than any conceivable classical computer. Just as classical information is encoded today in error-correcting codes to protect it against errors in transmission, quantum information will need to be encoded in quantum error-correcting codes in order to reliably reach its destination. Indeed, quantum information is more sensitive to errors than is classical information, so error correction will be even more important. On page 436 of this issue, Brun et al. (1) show how it is possible to improve the performance of quantum error-correcting codes, using a quantum state previously shared between the sender and receiver.
Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.
This paper presents the design of a communication protocol leveraging quantum error-correcting codes to enhance the reliability of quantum communication. The core idea revolves around encoding quantum information using a specific quantum error-correcting code and subsequently transmitting this encoded information. During transmission, the protocol employs error detection and correction techniques based on the chosen code to mitigate the detrimental effects of noise and decoherence, which are inherent challenges in quantum communication. The proposed protocol aims to significantly improve the robustness of quantum communication channels, a critical step towards realizing practical quantum networks and secure quantum key distribution. The theoretical framework and mathematical formulation of the protocol are presented, detailing the encoding process, error detection, and correction mechanisms. This work contributes to the growing field of quantum communication by providing a concrete design methodology for building more reliable quantum communication systems.
Quantum communication and information technologies are poised to transform secure data transmission, distributed quantum computing, and scalable networking by leveraging fundamental principles such as superposition, entanglement, and the no-cloning theorem. This survey presents a structured overview of the quantum information processing (QIP) landscape, spanning theoretical foundations to system-level architectures. We cover quantum states, unitary evolution, gates, and channels, leading to the mathematical framework of quantum operations and the effects of decoherence. Quantum error correction (QEC) is examined through block codes and fault-tolerant operations, along with its integration with entanglement purification to address challenges of noisy intermediate-scale quantum (NISQ) devices. Physical platforms, including gate-based, continuousvariable and measurement-based models, are analyzed with an emphasis on error mitigation strategies to preserve coherence. We also discuss advancements in quantum sensing, particularly phase estimation, and evaluate communication protocols such as quantum key distribution (QKD) and teleportation in terms of fidelity, efficiency, and resilience. At the system level, components such as quantum networks, repeaters, and routers are reviewed with attention to scalability and security. Each section concludes with lessons learned, reflecting on challenges, trade-offs, and open questions. The survey culminates in outlining future directions in hybrid QEC-sensing integration, AI-enhanced error correction, and topological architectures, offering a forward-looking perspective on the co-evolution of quantum technologies. By bridging theory, protocols, physical systems, and architectures, this work charts a comprehensive roadmap toward secure, scalable, and high-fidelity quantum communication.