Almost-quantum correlations violate the isotropy and homogeneity principles in flat space

One of fascinating phenomena of nature is quantum nonlocality, which is observed upon measurements on spacelike entangled systems. However, there are sets of post-quantum models which have stronger correlations than quantum mechanics, wherein instantaneous communication remains impossible. The set of almost quantum correlations is one of post-quantum models which satisfies all kinematic axioms of standard quantum correlations except one, meanwhile they contain correlations slightly stronger than quantum correlations. There arises the natural question whether there is some fundamental principle of nature which can genuinely characterizes quantum correlations. Here, we provide an answer and close this gap by invoking the isotropy and homogeneity principles of the flat space as a conclusive and distinguishing criterion to rule out the almost-quantum correlations model. In particular, to characterize quantum correlations we impose the isotropy and homogeneity symmetry group structure on the almost quantum correlations model and request that the joint probability distributions corresponding to the Born rule remain invariant. We prove that this condition is sufficient (and necessary) to reduce the almost quantum correlations model to quantum mechanics in both bipartite and multipartite systems.