| we investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global @xmath0-partite quantum state . intuitively , we say that the multipartite state `` joins '' the underlying correlations . determining whether , for a given set of states and a given joining structure , a compatible @xmath0-partite quantum state exists is known as the quantum marginal problem . we restrict to bipartite reduced states that belong to the paradigmatic classes of werner and isotropic states in @xmath1 dimensions , and focus on two specific versions of the quantum marginal problem which we find to be tractable . the first is alice - bob , alice - charlie joining , with both pairs being in a werner or isotropic state . the second is @xmath2-@xmath3 sharability of a werner state across @xmath0 subsystems , which may be seen as a variant of the @xmath0-representability problem to the case where subsystems are partitioned into two groupings of @xmath2 and @xmath3 parties , respectively . by exploiting the symmetry properties that each class of states enjoys , we determine necessary and sufficient conditions for three - party joinability and 1-@xmath3 sharability for arbitrary @xmath1 . our results explicitly show that although entanglement is required for sharing limitations to emerge , correlations beyond entanglement generally suffice to restrict joinability , and not all unentangled states necessarily obey the same limitations . the relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed . |