Abstract The promising future of the quantum internet hinges on how we scale entanglement distribution on quantum networks (QNs). Classical entanglement percolation (CEP) offers a simple approach for this but is limited by ‘classical’ scaling laws, while deterministic entanglement transmission (DET) leverages the determinacy of quantum protocols to achieve a more effective ‘quantum’ scaling. This advantage is, however, unexplored for Gaussian-state QNs, where the infinite-dimensional, continuous-variable states are often required to be first prepared into qubits or qudits via additional conversions. This overhead raises a question: can DET’s quantum advantage survive in a practical Gaussian-to-qudit conversion process? To answer this, we analyze both DET and CEP across a spectrum of conversion strategies, from best-case theoretical limits to probabilistic, practical projections. We find that DET’s superiority is robust: even a DET scheme burdened by the overhead of practical projective conversions consistently outperforms CEP endowed with theoretically perfect conversion. Our work thus provides a possible roadmap, demonstrating that the quantum-native approach of DET could be the key to unlocking the potential of long-range quantum communication.
Abstract The promising future of the quantum internet hinges on how we scale entanglement distribution on quantum networks (QNs). Classical entanglement percolation (CEP) offers a simple approach for this but is limited by ‘classical’ scaling laws, while deterministic entanglement transmission (DET) leverages the determinacy of quantum protocols to achieve a more effective ‘quantum’ scaling. This advantage is, however, unexplored for Gaussian-state QNs, where the infinite-dimensional, continuous-variable states are often required to be first prepared into qubits or qudits via additional conversions. This overhead raises a question: can DET’s quantum advantage survive in a practical Gaussian-to-qudit conversion process? To answer this, we analyze both DET and CEP across a spectrum of conversion strategies, from best-case theoretical limits to probabilistic, practical projections. We find that DET’s superiority is robust: even a DET scheme burdened by the overhead of practical projective conversions consistently outperforms CEP endowed with theoretically perfect conversion. Our work thus provides a possible roadmap, demonstrating that the quantum-native approach of DET could be the key to unlocking the potential of long-range quantum communication.
The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topology. More precisely, we implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary d-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized k-concurrences (a family of fundamental entanglement measures) for different QN topologies. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform.
Quantum entanglement as a non-local correlation between particles is critical to the transmission of quantum information in quantum networks (QNs); the key challenge lies in establishing long-distance entanglement transmission between distant targets. This issue aligns with percolation theory, and as a result, an entanglement distribution scheme called “Classical Entanglement Percolation” (CEP) has been proposed. While this scheme provides an effective framework, “Quantum Entanglement Percolation” (QEP) indicates a lower percolation threshold through quantum preprocessing strategies, which will modify the network topology. Meanwhile, an emerging statistical theory known as “Concurrence Percolation” reveals the unique advantages of quantum networks, enabling entanglement transmission under lower conditions. It fundamentally belongs to a different universality class from classical percolation. Although these studies have made significant theoretical advancements, most are based on an idealized pure state network model. In practical applications, quantum states are often affected by thermal noise, resulting in mixed states. When these mixed states meet specific conditions, they can be transformed into pure states through quantum operations and further converted into singlets with a certain probability, thereby facilitating entanglement percolation in mixed state networks. This finding greatly broadens the application prospects of quantum networks. This review offers a comprehensive overview of the fundamental theories of quantum percolation and the latest cutting-edge research developments.
Long-distance entanglement establishment is investigated on small-world complex network topologies.The quantum entanglement percolation(QEP) protocol is proposed to optimize networked quantum communications.If the additional local target-swap quantum operations are performed in the classical entanglement percolation(CEP) protocol,the QEP can be obtained.The QEP has great advantage over CEP with respect to the efficiency of long-distance entanglement establishment.The advantage may be due to the changes of the degree distributions in the QEP.
Quantum communication represents a revolutionary advancement over classical information theory, which leverages unique quantum mechanics properties like entanglement to achieve unprecedented capabilities in secure and efficient information transmission. Unlike bits in classical communication, quantum communication utilizes qubits in superposition states, allowing for novel information storage and processing. Entanglement, a key quantum phenomenon, enables advanced protocols with enhanced security and processing power. This paper provides a comprehensive overview of quantum communication, emphasizing the role of entanglement in theoretical foundations, practical protocols, experimental progress, and security implications. It contrasts quantum communications potential applications with classical networks, identifying areas where entanglement offers significant advantages. The paper explores the fundamentals of quantum mechanics in communication, the physical realization of quantum information, and the formation of secure quantum networks through entanglement-based strategies like Quantum Key Distribution (QKD) and teleportation. It addresses the challenges of long-distance quantum communication, the role of quantum repeaters in scaling networks, and the conceptualization of interconnected quantum networks. Additionally, it discusses strides towards the Quantum Internet, Quantum Error-Correcting codes, and quantum cryptographys role in ensuring secure communication. By highlighting the role of entanglement, this paper aims to inspire further research and innovation in secure and efficient information exchange within quantum networks.
Abstract Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes evolution of network connectivity with respect to some network parameters. In this framework, the probability to establish perfect entanglement between two remote partners decays exponentially with the distance between them before the percolation transition point, which unambiguously defines percolation properties of any classical network or lattice. Here we introduce quantum networks created with local operations and classical communication, which exhibit non-classical percolation transition points leading to striking communication advantages over those offered by the corresponding classical networks. We show, in particular, how to establish perfect entanglement between any two nodes in the simplest possible network—the 1D chain—using imperfectly entangled pairs of qubits.
The realization of entanglement distribution (ED) in large-scale quantum networks (QNs), as a fundamental theoretical framework of quantum communication, faces significant challenges. Percolation theory, drawn from statistical physics, has been identified as a potential solution to this problem. Nevertheless, when addressing ED, percolation theory primarily relies on numerical simulations and approximate algorithms. This approach often lacks interpretability and controllability for many phenomena occurring during the ED process in large-scale networks, including emergent phenomena near the threshold. To address these limitations, in this paper, we {focus on} leveraging operator theory to construct a mathematical framework for entanglement percolation in series-parallel QNs. Through the application of operator-theoretic methodologies, we analyze several critical issues within the entanglement percolation process.