Nonlocality as an axiom for quantum theory

Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate tile CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect). Can we invert the logical order? We consider a conjecture that nonlocality and relativistic causality together imply quantum mechanics. We show that correlations preserving relativistic causality can violate the CHSH inequality more strongly than quantum correlations. Also, we describe nonlocal equations of motion, preserving relativistic causality, that do not arise in quantum mechanics. In these nonlocal equations of motion, an experimenter ''jams'' nonlocal correlations between quantum systems.