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）利用紧凑天线阵列形成近乎连续的孔径，相比传统MIMO系统，能够实现更高的容量和更灵活的配置，因此在当前科学研究中备受关注。关于HMIMO能否超越香农理论极限及其能力可扩展至何种程度的关键问题随之产生。然而，传统香农信息理论在回答这些问题时存在不足，因其仅关注信息本身，而忽略了底层载体——电磁波以及环境相互作用。为填补HMIMO系统理论分析与实际应用之间的鸿沟，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，涵盖电磁波方程与通信区域。在HMIMO系统背景下，阐述了由此产生的物理限制，包括Chu极限、Harrington极限、Hannan极限以及耦合效应评估。同时讨论了场采样与HMIMO辅助的过采样，以指导EIT框架下的最优HMIMO设计。为全面描述符合电磁特性的传播过程，我们提出了近场/远场区域的近似与精确信道建模方法。此外，针对面向HMIMO的EIT系统，我们分别讨论了采用概率方法的传统香农信息理论，以及运用泛函分析的Kolmogorov信息理论。