We give a mathematical analysis of a new type of classical computer network architecture, intended as a model of a new technology that has recently been proposed in industry. Our approach is based on groubits, generalizations of classical bits based on groupoids. This network architecture allows the direct execution of a number of protocols that are usually associated with quantum networks, including teleportation, dense coding and secure key distribution.

• 20N02 - Sets with a single binary operation (groupoids)
• 68M10 - Network design and communication in computer systems
• 68M12 - Network protocols
• 81P68 - Quantum computation