Relational Quantum Dynamics as a Dagger Compact Category: A Categorical Framework for Awareness Transfer, No-Cloning, and Teleportation

We establish a rigorous connection between Relational Quantum Dynamics (RQD) and Categorical Quantum Mechanics (CQM) by formally showing that the category Q of quantum processes in RQD can be endowed with the structure of a dagger compact category. In particular, we demonstrate that Q satisfies the axioms of a dagger symmetric monoidal category with compact closure, mirroring the standard categorical formalism for quantum theory. Within this framework, key physical features of quantum mechanics, such as the transfer of awareness (information) in interactions, the no-cloning theorem, and the quantum teleportation protocol, are naturally expressed and interpreted. We define the categorical structures and illustrate the concepts with examples from quantum computing and quantum information. These examples highlight how RQD’s relational worldview aligns with CQM’s diagrammatic and algebraic characterization of quantum processes, thus providing a robust unified description. The results underscore that the RQD category Q not only has the formal properties of a dagger compact category but also that this structure provides clear insight into quantum informational tasks and no-go theorems, while incorporating the notion of observer-dependent reality in RQD via a functional mapping of awareness.