Fundamental Limits of Quantum Semantic Communication via Sheaf Cohomology
Christo Kurisummoottil Thomas, Mingzhe Chen
TL;DR
This work introduces a quantum semantic communication framework based on sheaf cohomology to model irreducible semantic ambiguities arising from heterogeneous agent representations. By promoting semantic spaces to quantum Hilbert spaces and channels to CPTP maps, the authors define quantum semantic sheaves and a Čech-based cohomology that isolates obstructions to global alignment. They derive a fundamental rate limit $R^*_{\text{sem}} = \log_2 \dim H^1(G, \mathcal{S})$ and show that entanglement reduces obstructions by $\sum_e \log_2 r_e$, while contextuality further lowers the required communication and quantum discord corresponds to integrated semantic information. The results provide a rigorous, topology-informed capacity-like theory for quantum-enhanced semantic communication in multi-agent systems, with implications for autonomous networks and AI alignment, and they outline directions for experimental validation and extensions to broader quantum regimes.
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.