Quantum Teleportation Using a Genuinely Classical Communication Channel Must Fail

During the quantum teleportation protocol, Alice sends two bits of classical information to Bob, which somehow transports quantum information from Alice's location to Bob's location. The local account of teleportation from Deutsch and Hayden reveals that these bits are actually qubits instantiating locally inaccessible information, and appear classical because they carry information in a form that is robust to decoherence. If the classical bits have absolutely no underlying quantum properties, teleportation will fail - challenging all current and future variants of quantum theory that explain teleportation using only classical properties of the physical bits being transported. A successful teleportation via apparently classical bits therefore indicates that either: (1) the fundamental principle of locality, which says that isolated systems are independent from each other, is false, or (2) the apparently classical bits actually have some quantum properties. We propose using existing models for quantum-classical dynamics, such as Sudarshan's, and the dynamics-independent Constructor Theory, to determine exactly what features a system with unknown dynamics needs to carry information for teleportation. Our proposal may characterise a new form of non-classicality, giving novel insights into hybrid quantum-classical systems. This could lead to new experimental proposals to test the properties of systems with unknown dynamics.