LAUSR

We analyze the structure of the space of temporal correlations generated by quantum systems. We show that the temporal correlation space under dimension constraints can be nonconvex, and derive nonlinear inequalities to witness the nonconvexity for qubits and qutrits in the simplest scenario. For the general case, we provide the necessary and sufficient dimension of a quantum system needed to generate a convex correlation space for a given scenario. We further prove that this dimension coincides with the dimension necessary to generate any point in the temporal correlation polytope. Finally, we present an algorithm which can help to find the minimum for a certain type of nonlinear expressions under dimension constraints.