Fundamental Limits of Quantum Semantic Communication via Sheaf Cohomology

2026-01-16

AI Summary

This work addresses the challenge of semantic alignment in heterogeneous multi-agent systems, where conventional bit-level communication fails to ensure mutual understanding and its information-theoretic limits remain unclear. The authors propose a quantum semantic communication framework grounded in sheaf cohomology, modeling semantic networks as quantum sheaves in Hilbert space interconnected via quantum channels. They employ the first cohomology group to characterize irreducible semantic ambiguities and reveal, for the first time, a homological correspondence between semantic ambiguity and quantum contextuality. An analog of Shannon’s limit for semantic alignment is established, proving that entanglement assistance can surpass classical capacity bounds. Furthermore, a duality is uncovered between quantum discord and integrated semantic information. The theory shows that the minimal communication rate scales logarithmically with the dimension of the cohomology space, and each shared ebit reduces classical communication cost by one bit, providing a rigorous foundation for quantum-enhanced semantic communication in autonomous multi-agent systems.

Technology Category

• Multiagent Systems: Agent Communication
• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Agentic search
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Semantic communication (SC) enables bandwidth-efficient coordination in multi-agent systems by transmitting meaning rather than raw bits. However, when agents employ heterogeneous sensing modalities and AI architectures, perfect bit-level transmission no longer guarantees mutual understanding. Although deep learning methods for semantic compression have advanced, the information-theoretic limits of semantic alignment under heterogeneity remain poorly understood. Notably, semantic ambiguity shares the same mathematical structure as quantum contextuality, as both arise from cohomological obstructions, motivating a quantum formulation of SC. In this paper, an information-theoretic framework for quantum semantic communication is proposed using sheaf cohomology. Multi-agent semantic networks are modeled as quantum sheaves, where agents meaning spaces are Hilbert spaces connected by quantum channels. The first sheaf cohomology group is shown to characterize irreducible semantic ambiguity, representing a fundamental obstruction to alignment that no local processing can resolve. The minimum communication rate required for semantic alignment is proven to scale with the logarithm of the dimension of the cohomological space, establishing a semantic analog of Shannon limits. For entanglement-assisted channels, the achievable capacity is shown to strictly exceed classical bounds, with each shared ebit reducing the required classical communication by one bit, providing a rigorous interpretation of shared context. Additionally, quantum contextuality is shown to reduce cohomological obstructions, and a duality between quantum discord and integrated semantic information is established, linking quantum correlations to irreducible semantic content. This framework provides rigorous foundations for quantum-enhanced semantic communication in autonomous multi-agent systems.

Problem

• semantic communication
• quantum contextuality
• sheaf cohomology
• semantic ambiguity
• heterogeneous multi-agent systems

Innovation

• sheaf cohomology
• quantum semantic communication
• semantic ambiguity
• quantum contextuality
• entanglement-assisted capacity