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Advanced Quantum Technologies

Toward Quantum‐Inspired Traffic Engineering: Mathematical Models for Minimal‐Disturbance Network Monitoring

Joachim Notcker, Domenico Scotece, Riccardo Bassoli, Luca Foschini, Frank H. P. Fitzek

Published Jun 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Network monitoring is fundamental to effective traffic engineering (TE) in quantum networks, as it provides a timely snapshot of network status. However, quantum measurement imposes intrinsic constraints: direct measurement of entangled states collapses the quantum state, and the no‐cloning theorem prohibits duplication of quantum information, rendering real‐time and continuous monitoring inherently challenging. Although nondestructive techniques such as weak measurement, quantum non‐demolition (QND) measurement, and protective measurement have been proposed, their roles in supporting TE have not been systematically examined within a unified framework. In this paper, we develop a unified analytical framework that integrates weak, QND, and protective measurements into TE‐driven quantum network monitoring, providing the first systematic network‐level analysis of these measurement paradigms in the context of quantum TE. We formulate their measurement models, characterize their information gain and disturbance trade‐offs, and evaluate their applicability in terms of measurement accuracy, real time response, scalability, overhead, and robustness to noise. We observe that although weak, QND, and protective measurement techniques offer theoretically compelling approaches for mitigating measurement‐induced back‐action, they remain constrained by significant practical limitations. Experimental complexity, scalability challenges, resource overhead, and latency considerations collectively limit their immediate suitability for deployment in real‐time quantum network monitoring frameworks supporting TE. We further distinguish between directly measurable and estimable network metrics, discuss their roles in TE, and analyze feasible measurement locations and timescales under coherence constraints. In addition, we present a formal definition of quantum traffic matrices and identify four key types of network knowledge inferred from data analysis and provide a formal definition and framework for the characterization of entanglement availability. Finally, our work lays a solid foundation and outlines a clear roadmap for achieving TE in quantum networks, while carefully accounting for the fundamental limitations imposed by quantum measurements and the no‐cloning theorem.

DOI
10.1002/qute.202500635

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ABSTRACT Network monitoring is fundamental to effective traffic engineering (TE) in quantum networks, as it provides a timely snapshot of network status. However, quantum measurement imposes intrinsic constraints: direct measurement of entangled states collapses the quantum state, and the no‐cloning theorem prohibits duplication of quantum information, rendering real‐time and continuous monitoring inherently challenging. Although nondestructive techniques such as weak measurement, quantum non‐demolition (QND) measurement, and protective measurement have been proposed, their roles in supporting TE have not been systematically examined within a unified framework. In this paper, we develop a unified analytical framework that integrates weak, QND, and protective measurements into TE‐driven quantum network monitoring, providing the first systematic network‐level analysis of these measurement paradigms in the context of quantum TE. We formulate their measurement models, characterize their information gain and disturbance trade‐offs, and evaluate their applicability in terms of measurement accuracy, real time response, scalability, overhead, and robustness to noise. We observe that although weak, QND, and protective measurement techniques offer theoretically compelling approaches for mitigating measurement‐induced back‐action, they remain constrained by significant practical limitations. Experimental complexity, scalability challenges, resource overhead, and latency considerations collectively limit their immediate suitability for deployment in real‐time quantum network monitoring frameworks supporting TE. We further distinguish between directly measurable and estimable network metrics, discuss their roles in TE, and analyze feasible measurement locations and timescales under coherence constraints. In addition, we present a formal definition of quantum traffic matrices and identify four key types of network knowledge inferred from data analysis and provide a formal definition and framework for the characterization of entanglement availability. Finally, our work lays a solid foundation and outlines a clear roadmap for achieving TE in quantum networks, while carefully accounting for the fundamental limitations imposed by quantum measurements and the no‐cloning theorem.
In today’s fast-evolving technological landscape, the Internet of Things (IoT) is fundamentally reshaping how systems connect, interact, and exchange data. As billions of devices become interconnected, the IoT brings both unprecedented opportunities and significant challenges across various domains. Emerging technologies, particularly quantum communication networks, offer transformative solutions by enabling ultra-secure data exchange within IoT infrastructures through advanced techniques such as Quantum Key Distribution (QKD). However, quantum link delay remains one of the key challenges that hinder the effective utilization of these networks. Traffic engineering is a robust method to address this challenge and optimize the performance of quantum networks. This technique involves assessing the current state of the network and making dynamic adjustments based on real-time conditions. Despite its proven benefits in classical systems, its role in quantum networks remains largely unexplored, with no comprehensive framework to date. As a result, in this paper, we propose a framework for quantum traffic engineering and discuss its core components—non-invasive measurements, quantum traffic matrices, data analysis, and performance control. Additionally, we integrate the Particle Swarm Optimization (PSO) algorithm into our framework to minimize the quantum link delay. Ultimately, this work establishes the foundation for researchers in quantum network traffic engineering and sets the stage for continuous, and dynamic monitoring of these networks.
In today’s fast-evolving technological landscape, the Internet of Things (IoT) is fundamentally reshaping how systems connect, interact, and exchange data. As billions of devices become interconnected, the Internet of Things brings unprecedented opportunities and significant challenges in various domains. Emerging technologies, particularly quantum communication networks, offer transformative solutions by enabling ultra-secure data exchange within IoT infrastructures through advanced techniques such as quantum key distribution. However, a significant obstacle to the efficient use of these networks is the lack of current status knowledge of network parameters, which is essential for continuous and dynamic management through quantum traffic engineering. In this paper, we propose the novel concept of quantum traffic matrices as a foundational framework to capture the dynamic operational state of quantum networks. We begin by distinguishing classical traffic matrices from their quantum counterparts. We then identify and present mathematical models for eleven key quantum network parameters that are essential to enable continuous and dynamic management of quantum networks. Our approach and results serve as crucial input for the development of quantum traffic engineering strategies, paving the way for intelligent control, optimization, and resilience enhancement of future quantum communication infrastructures.
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Quantum traffic engineering is a revolutionary approach envisioned to give optimum solutions to network-related difficulties in quantum networks such as entanglement routing, resource management and so on. However, the crucial input to these strategies is traffic matrix. The traffic matrices (Fidelity and channel capacity matrices) provide the knowledge about the network which enables network engineers to apply reliable and resilient solutions to optimize the performance of quantum networks. There are extensive works of traffic matrix estimation in classical networks, however there is no work in literature that explain how to construct traffic matrices in quantum networks. In this work, we provide comprehensive step-by-step guidance for creating quantum traffic matrices. Moreover, we examine the effects of data analysis on traffic matrices that have been developed. Based on our findings, we observe that the fidelity matrix is significantly impacted by the methods used to execute quantum state reconstruction during data analysis, while the capacity matrix is significantly impacted by the likelihood that channels will be successfully distinguished.
We develop a comprehensive theoretical framework for analyzing quantum information flow in networked quantum systems with emphasis on entanglement distribution and temporal correlation structures. Drawing from recent applications in real-time sensing and detection systems, we formulate a general mathematical model that describes how quantum correlations propagate through network topologies and evolve over time. The framework incorporates decoherence effects, network connectivity constraints, and measurement-induced state collapse to provide realistic bounds on information transmission capabilities. We derive analytical expressions for entanglement generation rates, fidelity preservation across network hops, and temporal correlation decay under various noise models. The theory establishes fundamental limits on the capacity of quantum networks to maintain coherent information transfer and identifies optimal network architectures for specific correlation preservation requirements. We extend our analysis to adaptive network configurations where topology can be dynamically adjusted based on environmental conditions or information priorities. The theoretical results provide design principles for quantum communication protocols, distributed quantum sensing arrays, and real-time quantum-enhanced detection systems, bridging fundamental quantum information theory with practical networked applications.
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