quantum channel modeling and analysis

The non-additivity of quantum channel capacity fundamentally impedes its computation and practical application, necessitating asymptotic regularization and thereby undermining the elegance and utility of quantum Shannon theory. To address this, we refine the communication scenario by incorporating physically natural constraints—namely, restricted auxiliary resources and operational limitations—thereby defining a novel class of capacity measures. Within this framework, we rigorously establish additivity for several fundamental quantum channels, including depolarizing and erasure channels, eliminating the need for regularization entirely. Our analysis, grounded in the von Neumann entropy, yields closed-form expressions for these capacities, drastically simplifying evaluation. Moreover, it reinforces the centrality of entropy in quantum information foundations. By providing analytically tractable, operationally meaningful capacity measures, our approach furnishes a more robust and implementable physical basis for quantum Shannon theorems.

This work addresses the problem of bounding the quantum and private capacities of noisy quantum channels—specifically amplitude-damping and depolarizing channels—and characterizing their zero-capacity thresholds. Methodologically, we introduce a novel flagged extension technique to construct high-dimensional embeddings, yielding tight single-letter upper bounds; we further integrate Bloch sphere parameterization with numerical coherent-information optimization to enable efficient input-state search and capacity estimation. Our key contributions include: (i) the first systematic verification that the amplitude-damping channel satisfies single-letter additivity of coherent information; (ii) the first rigorous demonstration of strong multi-letter superadditivity for the depolarizing channel; and (iii) precise numerical determination of the noise thresholds at which both quantum and private capacities vanish, with error < 10⁻⁴. These results provide foundational criteria and a practical computational framework for quantum channel capacity theory.

Quantum computing poses a critical threat to classical cryptographic systems, necessitating scalable, interoperable quantum key distribution (QKD) networks. Method: This paper proposes a model-based systems engineering (MBSE) approach for scalable QKD network design, introducing variability-driven architecture modeling. It integrates orthogonal variability modeling with SysML to jointly model and co-design QKD systems and classical communication infrastructure. Contribution/Results: The resulting modular, traceable architecture enables rapid evolution and cross-scenario reuse, significantly enhancing network adaptability and development efficiency. Standardized architectural artifacts—including variability models, system interfaces, and integration patterns—are produced, serving as a reference model for QKD network deployment. Furthermore, the framework supports broader integration and evolutionary research of quantum information systems, facilitating interoperability between quantum and classical infrastructures.

This study investigates the computability and computational complexity of quantum channel capacities. By leveraging tools from quantum complexity theory and undecidability analysis, it rigorously establishes for the first time that computing the quantum capacity of a general quantum channel is QMA-hard. Furthermore, it demonstrates that the zero-error one-shot classical capacity assisted by maximal entanglement is uncomputable. These results resolve a fundamental open question in quantum information theory concerning the computability of channel capacities and provide crucial theoretical underpinnings for quantum communication.

This work addresses the lack of efficient numerical methods for computing the quantum channel relative entropy—a fundamental metric in quantum channel discrimination and resource theories. Methodologically, we introduce the first scalable, error-controllable computational framework: we discretize and linearize the integral representation of quantum state relative entropy, thereby reformulating the channel relative entropy maximization problem as a sequence of semidefinite programs (SDPs); tight upper and lower bounds are constructed to enable arbitrarily precise sandwich estimation. Crucially, our approach overcomes prior limitations restricted to minimization settings, enabling rigorous optimization over input states for the first time. Experiments demonstrate high accuracy and low computational complexity, significantly enhancing the tractability and practical utility of channel relative entropy in real-world discrimination tasks and resource quantification.

Existing model synchronization approaches struggle to accommodate the superposition and entanglement inherent in quantum systems, thereby failing to ensure consistency across heterogeneous models from multiple domains. To address this challenge, this work proposes QSysMM—the first dedicated model management framework tailored for engineered quantum systems—which establishes a unified digital single source of truth by harmonizing quantum engineering models along four dimensions: ontology, abstraction, composition, and exposure. Built upon the SysML v2 technology stack, we introduce QSysML, a companion modeling language that integrates model-driven engineering with quantum information science to preserve quantum semantics throughout model transformations. This framework provides a comprehensive foundation for the construction, verification, and maintenance of complex quantum systems through robust model synchronization and management.

This work addresses the absence of a unified, reusable operational framework in quantum information theory for formally capturing encodings, error criteria, and capacity notions— a gap that has impeded machine verification of foundational theorems. To bridge this, the authors develop LeanQIT, a formal library in Lean 4 that, for the first time, decouples operational semantics from information-theoretic characterizations, offering composable and kernel-verified interfaces. The library enables modular formalization of quantum states, channels, encodings, hypothesis testing, and both single-shot and asymptotic analyses. It has been successfully employed to verify key results including Schumacher’s source coding theorem, the Holevo–Schumacher–Westmoreland classical capacity theorem, its entanglement-assisted variant, and the corresponding strong converse theorem, thereby laying a rigorous foundation for AI-assisted reasoning in quantum information theory.

This work addresses the limitation of conventional confusability graphs in fully characterizing the indistinguishability of input states in quantum channels. To overcome this, the authors propose a novel “quantum confusability multigraph” model that embeds channel output information into a graph structure, where multiple edges between vertices recover classical confusability relations. Building upon Weaver’s theory of quantum relations, they establish a rigorous mathematical framework for this model. The study establishes, for the first time, a one-to-one correspondence between quantum confusability multigraphs and quantum channels, and provides necessary and sufficient conditions for the existence of such multigraphs. This result fully characterizes the structural properties of confusability multigraphs realizable by quantum channels, thereby extending the applicability of quantum graph theory to problems of information distinguishability.

This work addresses the scarcity of quantum network hardware and the limitations of existing simulation tools in efficiently and accurately co-simulating quantum operations and classical signaling. To this end, the authors present Q2NS, a modular and extensible quantum network simulator built on ns-3. Q2NS introduces an architecture that decouples protocol control logic from node and channel operations, and uniformly supports multiple quantum state representations—including state vectors, density matrices, and stabilizer formalisms—while enabling tightly integrated simulation of quantum and classical communication. The framework also provides dedicated visualization tools to facilitate rapid prototyping of heterogeneous quantum internet scenarios. Experimental evaluations demonstrate that Q2NS achieves high computational efficiency and modeling flexibility across real-world use cases and benchmark tests, offering an open-source platform for quantum internet research.

This work addresses the critical challenge of scaling quantum networks from laboratory prototypes to programmable, multi-tenant global infrastructures by co-designing physical-layer capabilities with network engineering principles. It proposes a network-centric architecture featuring a novel dual-plane design for Software-Defined Quantum Networking (SDQN) and a Quantum Network Operating System (QNOS), enabling efficient coordination between classical control and quantum data planes. Furthermore, the paper introduces a Quantum Network Utility Maximization (Q-NUM) framework that jointly optimizes entanglement routing, scheduling, and fidelity trade-offs. By bridging the gap between simulation and real-world deployment, this research provides network engineers with a comprehensive toolchain and reference model to build scalable quantum networks under practical constraints such as decoherence and probabilistic delays.