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arXiv:2309.12907 · Physical Review Letters

Certifying the Topology of Quantum Networks: Theory and Experiment

Lisa T. Weinbrenner, Nidhin Prasannan, Kiara Hansenne, Sophia Denker, Jan Sperling, Benjamin Brecht, Christine Silberhorn, Otfried Gühne

Published Jun 11, 2024• 15 citations
arXivHTMLPDF

Abstract

Distributed quantum information in networks is paramount for global secure quantum communication. Moreover, it finds applications as a resource for relevant tasks, such as clock synchronization, magnetic field sensing, and blind quantum computation. For quantum network analysis and benchmarking of implementations, however, it is crucial to characterize the topology of networks in a way that reveals the nodes between which entanglement can be reliably distributed. Here, we demonstrate an efficient scheme for this topology certification. Our scheme allows for distinguishing, in a scalable manner, different networks consisting of bipartite and multipartite entanglement sources. It can be applied to semi-device-independent scenarios also, where the measurement devices and network nodes are not well characterized and trusted. We experimentally demonstrate our approach by certifying the topology of different six-qubit networks generated with polarized photons, employing active feed-forward and time multiplexing. Our methods can be used for general simultaneous tests of multiple hypotheses with few measurements, being useful for other certification scenarios in quantum technologies.

DOI
10.1103/physrevlett.132.240802

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Distributed quantum information in networks is paramount for global secure quantum communication. Moreover, it finds applications as a resource for relevant tasks, such as clock synchronization, magnetic field sensing, and blind quantum computation. For quantum network analysis and benchmarking of implementations, however, it is crucial to characterize the topology of networks in a way that reveals the nodes between which entanglement can be reliably distributed. Here, we demonstrate an efficient scheme for this topology certification. Our scheme allows for distinguishing, in a scalable manner, different networks consisting of bipartite and multipartite entanglement sources. It can be applied to semi-device-independent scenarios also, where the measurement devices and network nodes are not well characterized and trusted. We experimentally demonstrate our approach by certifying the topology of different six-qubit networks generated with polarized photons, employing active feed-forward and time multiplexing. Our methods can be used for general simultaneous tests of multiple hypotheses with few measurements, being useful for other certification scenarios in quantum technologies.
The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as a definition of genuine multipartite quantum steering, give a method to detect entanglement in a scenario in between the standard entanglement and fully device-independent scenarios, and provide a basis for semi-device-independent cryptographic applications in quantum networks.
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.
Fully connected quantum networks enable scalable quantum communication, yet reliable entanglement characterization without trusting measurement devices remains challenging. Here we experimentally demonstrate measurement-device-independent (MDI) entanglement verification and quantification in a time-bin-encoded fully connected quantum network. Using a broadband periodically poled lithium niobate on insulator source combined with dense wavelength-division multiplexing, we distribute all six pairwise entangled links among four users over 20-km fiber channels, preserving high-fidelity entanglement without active stabilization of the long-distance fiber links. We show that conventional entanglement witnesses can fail under untrusted measurement conditions. By encoding trusted input states in the polarization degree of freedom of the same photons, we realize MDI measurements without ancillary photons or additional experimental resources. Both entanglement verification and quantification are obtained from the same measurement dataset. Our results establish a practical and scalable approach for reliable entanglement characterization in quantum networks.
Quantum correlation between nodes in a network which consist of several independent sources of entanglement and in multipartite entanglement systems are important for general understanding of the nature of nonlocality, quantum information processing and communication. In previous years, demonstrations of network nonlocality for bilocal scenarios have been in the focus. Yet, it has been found that the seminal protocols do not certify entanglement between end nodes, which otherwise require all sources in the network to be of nonlocal nature. This has motivated for development of even stronger concept, called full network nonlocality. Here, we experimentally demonstrate full network nonlocal correlations in a network. Specifically, we use two pairs of polarization entangled qubits created by two separate and independent entanglement sources and a partial Bell state measurement. Our results may pave the way for the use of nonlocality test in quantum communication protocols with a full network nonlocality certification.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
Paramount for performances of quantum network applications are the structure and quality of distributed entanglement. Here we propose a scalable and efficient approach to reveal the topological information of unknown quantum networks, and quantify entanglement simultaneously. The scheme exploits entropic uncertainty, an operationally meaningful measure of correlation, by performing only two local measurements on each qubit. Moreover, when measurement outcomes in each node are collectively evaluated, integrating uncertainty and mutual information enables a direct count of the number of bipartite sources between any two nodes. This surpasses what is possible via applying either approach solely. Moreover, quantum error mitigation techniques including probabilistic error cancellation (PEC) and virtual distillation (VD), which have been widely applied to suppress biases in single expectation value, are further incorporated to mitigate errors in entropic quantities. We find that PEC successfully removes deviations in correlation estimations. Meanwhile, VD extends the depolarizing noise strength that allows for valid bipartite entanglement certification from 8.8% to 26.4%, thus substantially enhancing robustness against bias-inducing noise in practical situations. The proposal is applicable to a broad variety of platforms and helps to spur future studies toward harnessing the advantages of quantum networks.