The development of large-scale quantum communication networks necessitates the efficient distribution of quantum states to enable advanced cryptographic applications and distributed tasks. Multipartite entanglement is a key resource in many of these proposals, yet its generation is experimentally challenging, especially in noisy and lossy networks. While a substantial body of work focuses on the distribution of multi-partite entanglement in star-like topologies, practical implementations often rely on linear network structures constrained by existing infrastructure. In this work, we investigate the generation of high-fidelity multipartite entangled states in a realistic quantum network, leveraging the existing infrastructure of the Q-net-Q project-a real-world long-distance link connecting Berlin and Frankfurt via seven trusted relay nodes. Given that only bipartite entanglement sources are available in our setting and that the network is highly lossy, we explore the role of quantum memories in enhancing multi-partite entanglement distribution and identify key performance requirements. Furthermore, we analyze the feasibility and performance of cryptographic primitives-including (Anonymous) Conference Key Agreement and Quantum Secret Sharing-highlighting the scenarios where the use of multipartite entanglement yields clear advantages.
The development of large-scale quantum communication networks necessitates the efficient distribution of quantum states to enable advanced cryptographic applications and distributed tasks. Multipartite entanglement is a key resource in many of these proposals, yet its generation is experimentally challenging, especially in noisy and lossy networks. While a substantial body of work focuses on the distribution of multi-partite entanglement in star-like topologies, practical implementations often rely on linear network structures constrained by existing infrastructure. In this work, we investigate the generation of high-fidelity multipartite entangled states in a realistic quantum network, leveraging the existing infrastructure of the Q-net-Q project-a real-world long-distance link connecting Berlin and Frankfurt via seven trusted relay nodes. Given that only bipartite entanglement sources are available in our setting and that the network is highly lossy, we explore the role of quantum memories in enhancing multi-partite entanglement distribution and identify key performance requirements. Furthermore, we analyze the feasibility and performance of cryptographic primitives-including (Anonymous) Conference Key Agreement and Quantum Secret Sharing-highlighting the scenarios where the use of multipartite entanglement yields clear advantages.
Distribution and distillation of entanglement over quantum networks is a basic task for Quantum Internet applications. A fundamental question is then to determine the ultimate performance of entanglement distribution over a given network. Although this question has been extensively explored for bipartite entanglement-distribution scenarios, less is known about multipartite entanglement distribution. Here we establish the fundamental limit of distributing multipartite entanglement, in the form of GHZ states, over a quantum network. In particular, we determine the multipartite entanglement distribution capacity of a quantum network, in which the nodes are connected through lossy bosonic quantum channels. This setting corresponds to a practical quantum network consisting of optical links. The result is also applicable to the distribution of multipartite secret key, known as common key, for both a fully quantum network and trusted-node based quantum key distribution network. Our results set a general benchmark for designing a network topology and network quantum repeaters (or key relay in trusted nodes) to realize efficient GHZ state/common key distribution in both fully quantum and trusted-node-based networks. We show an example of how to overcome this limit by introducing a network quantum repeater. Our result follows from an upper bound on distillable GHZ entanglement introduced here, called the "recursive-cut-and-merge" bound, which constitutes major progress on a longstanding fundamental problem in multipartite entanglement theory. This bound allows for determining the distillable GHZ entanglement for a class of states consisting of products of bipartite pure states.
This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular.We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings.The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement.First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links).We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem.We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement.Second, we consider a mixed-state definition of the connections of the quantum networks.This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs.New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations.Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance.Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a few links only.Based on the theory of random graphs, we propose a model of quantum complex networks, which exhibit some totally unexpected properties compared to their classical counterparts.5.1 Propagation of a large GHZ state through the lattice . . .5.2 Bit-flip error correction . . . . . . . . . . . . .
Secret sharing is a multiparty cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed).When sharing classical secrets (as opposed to quantum states), one can distinguish between protocols that leverage bipartite quantum key distribution (QKD) and those that exploit multipartite entanglement.The latter class are known to be vulnerable to so-called participant attacks and, while progress has been made recently, there is currently no analysis that quantifies their performance in the composable, finite-size regime, which has become the gold standard for QKD security.Given this-and the fact that distributing multipartite entanglement is typically challenging-one might well ask is there any virtue in pursuing multipartite entanglement-based schemes?Here, we answer this question in the affirmative for a class of secret-sharing protocols based on continuous-variable graph states.We establish security in a composable framework and identify a network topology, specifically a bottleneck network of lossy channels, and parameter regimes within the reach of present-day experiments for which a multipartite scheme outperforms the corresponding QKD-based method in the asymptotic and finite-size setting.Finally, we establish experimental parameters where the multipartite schemes outperform any possible QKD-based protocol.This is one of the first concrete compelling examples of multipartite entangled resources achieving a genuine advantage over point-to-point protocols for quantum communication and represents a rigorous, operational benchmark to assess the usefulness of such resources.
Quantum networks connect systems at separate locations via quantum links, enabling a wide range of quantum information tasks between distant parties. Large-scale networks have the potential to enable global secure communication, distributed quantum computation, enhanced clock synchronization, and high-precision multiparameter metrology. For the optimal development of these technologies, however, it is essential to identify the necessary resources and sub-routines that will lead to the quantum advantage, but this is demanding even for the simplest protocols in quantum information processing. Here we show that quantum networks relying on the long-distance distribution of bipartite entanglement, combined with local operations and shared randomness, cannot achieve a relevant quantum advantage. Specifically, we prove that these networks do not help in preparing resourceful quantum states such as Greenberger-Horne-Zeilinger states or cluster states, despite the free availability of long-distance entanglement. At an abstract level, our work points towards a fundamental difference between bipartite and multipartite entanglement. From a practical perspective, our results highlight the need for classical communication combined with quantum memories to fully harness the power of quantum networks.
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, quantum networks can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph-based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
Scaling the number of entangled nodes in a quantum network is a challenge with significant implications for quantum computing, clock synchronisation, secure communications, and quantum sensing. In a quantum network, photons interact with matter qubits at different nodes, flexibly enabling the creation of remote entanglement between them. Multipartite entanglement among multiple nodes will be crucial for many proposed quantum network applications, including quantum computational tasks and quantum metrology. To date, experimental efforts have primarily focused on generating bipartite entanglement between nodes, which is widely regarded as the fundamental quantum resource for quantum networks. However, relying exclusively on bipartite entanglement to form more complex multipartite entanglement introduces several challenges. These include the need for ancillary qubits, extensive local entangling operations which increases the preparation latency, and increasingly stringent requirements on coherence times as the number of nodes grows. Here, we analyse various schemes that achieve multipartite entanglement between nodes in a single step, bypassing the need for multiple rounds of bipartite entanglement. We demonstrate that different schemes can produce distinct multipartite entangled states, with varying fidelity and generation rates. Additionally, we discuss the applicability of these schemes across different experimental platforms, highlighting their primary advantages and disadvantages.