We investigate the existence of secure bit commitment protocols in the convex framework for probabilistic theories. The framework makes only minimal assumptions, and can be used to formalize quantum theory, classical probability theory, and a host of other possibilities. We prove that in all such theories that are locally non-classical but do not have entanglement, there exists a bit commitment protocol that is exponentially secure in the number of systems used.
Barnum, H., Dahlsten, O.C.O., Leifer, M., Toner, B. 2008. Nonclassicality without Entanglement Enables Bit Commitment. Proceedings of IEEE Information Theory Workshop, 2008, 386—390.