  We introduce a fundamental concept -- closed sets of correlations -- for
studying non-local correlations. We argue that sets of correlations
corresponding to information-theoretic principles, or more generally to
consistent physical theories, must be closed under a natural set of operations.
Hence, studying the closure of sets of correlations gives insight into which
information-theoretic principles are genuinely different, and which are
ultimately equivalent. This concept also has implications for understanding why
quantum non-locality is limited, and for finding constraints on physical
theories beyond quantum mechanics.
