The fundamental understanding of quantum systems and their correlations, as well as their characterization and quantification are crucial for modern information processing and communication. Conventionally, the quantum information being processed is encoded either in discrete or continuous degrees of freedom. Qubits and harmonic oscillators are essential parts of quantum devices employed for the effective transmission and storage of quantum information, and also of optimal quantum engines. Accordingly, the dimension of a system, finite or infinite, plays a key role in the information‐processing capacity of such devices. These two types of systems have fundamentally different mathematical descriptions that marks a consistent division within the quantum information community. Objectives and approach: We aim to strengthen an alliance between the two parts, advancing in the informational‐theoretic study of infinite‐dimensional systems, identifying better resources for reliable tomography of continuous‐variable systems, understanding the definite role of discretization strategies for their characterization, exploring unified descriptions for complex continuous‐discrete hybrid systems, and progressing in the optimization of current resources for optimal measurements and data post‐processing. There are multiple aspects of infinite‐dimensional systems we would like to address. We would like to find an optimal discretization strategy and their effective dimension needed for reliable certification of their quantum properties, the corresponding sampling, measurement, and post‐processing complexity, and to provide the scaling of error rates. In addition, we want to find an efficient and consistent way of characterizing and quantifying continuous‐discrete correlations and to reveal the cost of the exchange of quantum information between the discrete and continuous degrees of freedom of hybrid systems. These quantumness measures will be formulated within an operational framework of experimentally friendly witnesses. Innovation: The overall goal of our proposal is to find optimal strategies to identify and exploit all the benefits of infinite‐dimensional systems from an information‐theoretical point of view. What we want is to compare, merge, and go beyond both independent, discrete and continuous variable, approaches and thus to explore new scenarios. We ambition to develop unified and accessible theoretical methods for characterizing, verifying, and benchmarking the quantum properties of such hybrid systems.