Holographic multiple-input multiple-output (HMIMO) utilizes a compact antenna array to form a nearly continuous aperture, thereby enhancing higher capacity and more flexible configurations compared with conventional MIMO systems, making it attractive in current scientific research. Key questions naturally arise regarding the potential of HMIMO to surpass Shannon's theoretical limits and how far its capabilities can be extended. However, the traditional Shannon information theory falls short in addressing these inquiries because it only focuses on the information itself while neglecting the underlying carrier, electromagnetic (EM) waves, and environmental interactions. To fill up the gap between the theoretical analysis and the practical application for HMIMO systems, we introduce electromagnetic information theory (EIT) in this paper. This paper begins by laying the foundation for HMIMO-oriented EIT, encompassing EM wave equations and communication regions. In the context of HMIMO systems, the resultant physical limitations are presented, involving Chu's limit, Harrington's limit, Hannan's limit, and the evaluation of coupling effects. Field sampling and HMIMO-assisted oversampling are also discussed to guide the optimal HMIMO design within the EIT framework. To comprehensively depict the EM-compliant propagation process, we present the approximate and exact channel modeling approaches in near-/far-field zones. Furthermore, we discuss both traditional Shannon's information theory, employing the probabilistic method, and Kolmogorov information theory, utilizing the functional analysis, for HMIMO-oriented EIT systems.

翻译：全息多输入多输出（HMIMO）利用紧凑的天线阵列形成近似连续的孔径，从而相较于传统MIMO系统实现了更高容量和更灵活的配置，使其在当今科学研究中备受关注。自然会产生关键问题：HMIMO是否有可能超越香农理论极限，以及其能力能扩展至何种程度。然而，传统香农信息论难以回答这些问题，因为它仅关注信息本身，而忽略了底层载体——电磁波——以及环境相互作用。为弥合HMIMO系统理论分析与实际应用之间的差距，本文引入了电磁信息理论（EIT）。本文首先为面向HMIMO的EIT奠定基础，涵盖电磁波方程和通信区域。在HMIMO系统背景下，提出了由此产生的物理限制，包括楚氏极限、哈林顿极限、汉南极限以及耦合效应评估。还讨论了场采样和HMIMO辅助过采样，以指导EIT框架下的最优HMIMO设计。为全面描述符合电磁规律的传播过程，本文提出了近场区和远场区中的近似与精确信道建模方法。此外，针对面向HMIMO的EIT系统，本文讨论了采用概率方法的传统香农信息论以及运用泛函分析的科尔莫戈罗夫信息论。