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We show that generic pure states (states drawn according to the Haar measure)of four particles of equal internal dimension are uniquely determined among allother pure states by their two-body marginals. In fact, certain subsets ofthree of the two-body marginals suffice for the characterization. We alsodiscuss generalizations of the statement to pure states of more particles,showing that these are almost always determined among pure states by three oftheir $(n-2)$-body marginals. Finally, we present special families of symmetricpure four-particle states that share the same two-body marginals and aretherefore undetermined. These are four-qubit Dicke states in superposition withgeneralized GHZ states.

Almost all four-particle pure states are determined by their two-body marginals