In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, do support a teleportation protocol. We isolate a natural class of composite systems that we term regular, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields a large supply of theories, neither classical nor quantum, that support such a protocol.
Barnum, H., Barrett, J., Leifer, M., Wilce, A. 2012. Teleportation in General Probabilistic Theories. Mathematical Foundations of Information Flow: Proceedings of the Clifford Lectures 2008, Proceedings of Symposia in Applied Mathematics, 71, 25-47.
American Mathematical Society