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.

翻译：语义通信通过传输意义而非原始比特，实现了多智能体系统中的带宽高效协同。然而，当智能体采用异构的感知模态与人工智能架构时，完美的比特级传输不再保证相互理解。尽管用于语义压缩的深度学习方法已取得进展，但异构条件下语义对齐的信息论极限仍鲜为人知。值得注意的是，语义模糊性与量子语境性具有相同的数学结构，两者均源于上同调障碍，这为语义通信的量子化表述提供了动机。本文提出了一种基于层上同调的量子语义通信信息论框架。多智能体语义网络被建模为量子层，其中智能体的意义空间是通过量子信道连接的希尔伯特空间。研究表明，第一层上同调群刻画了不可约的语义模糊性，代表了一种无法通过任何局部处理解决的对齐基本障碍。语义对齐所需的最小通信速率被证明与上同调空间维数的对数成正比，从而建立了香农极限的语义类比。对于纠缠辅助信道，可达容量被证明严格超越经典界限，每个共享的纠缠比特可将所需的经典通信减少一个比特，这为共享语境提供了严格的解释。此外，量子语境性被证明可减少上同调障碍，并且建立了量子失谐与集成语义信息之间的对偶关系，从而将量子关联与不可约的语义内容联系起来。该框架为自主多智能体系统中的量子增强语义通信奠定了严格的理论基础。