Universal Bell Correlations Do Not Exist

We prove that there is no finite-alphabet nonlocal box that generates exactly those correlations that can be generated using a maximally entangled pair of qubits. More generally, we prove that if some finite-alphabet nonlocal box is strong enough to simulate arbitrary local projective measurements of a maximally entangled pair of qubits, then that nonlocal box cannot itself be simulated using any finite amount of entanglement. We also give a quantitative version of this theorem for approximate simulations, along with a corresponding positive result.

Bell's theorem says that (roughly) given the laws of quantum mechanics, it follows that two parties can interact instantaneously across arbitrary distances. This phenomenon ("quantum nonlocality") is amazing, but the nature of the "interactions" is notoriously subtle. Quantum nonlocality provably cannot be used to communicate, but it can be used to coordinate in certain surprising ways.

In this paper, we rule out one possible approach to characterizing the exact extent of the "nonlocal powers" granted by the laws of quantum mechanics. In particular, aside from quantum nonlocality, another situation in which two parties can interact in a limited way is if there is some discrete, classical device that each party is able to interact with. We prove that quantum nonlocality is not quite equivalent to any such discrete, classical device.