All-quantum mode-adaptable communication processors: mathematical frameworks

The rapid expansion and diversity of quantum communication protocols are accelerating the development of the Quantum Internet-a global network interconnecting heterogeneous quantum communication nodes and systems. A key challenge in this effort is achieving all-quantum mode adaptation, which is essential for enabling interoperability among quantum nodes and enhancing the efficiency and scalability of quantum information transmission. This paper introduces a mathematical framework for all-quantum mode adaptation, centered on three core mechanisms: mode expansion, mode reduction, and mode mapping. These processes are fundamental to managing compatibility across different quantum signal encodings. By leveraging multiple degrees of freedom (DoFs) of photons, such as time, path, and polarization, we demonstrate the feasibility of mode-adaptable all-quantum processors capable of dynamically interfacing with varied quantum communication environments. Our results address critical real-world challenges in building a flexible, scalable, and interoperable Quantum Internet, laying a basis for architecture-level integration of heterogeneous quantum technologies.