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We define the type-independent resource theory of local operations and sharedentanglement (LOSE). This allows us to formally quantify postquantumness incommon-cause scenarios such as the Bell scenario. Any nonsignaling bipartitequantum channel which cannot be generated by LOSE operations requires apostquantum common cause to generate, and constitutes a valuable resource. Ourframework allows LOSE operations that arbitrarily transform between differenttypes of resources, which in turn allows us to undertake a systematic study ofthe different manifestations of postquantum common causes. Only three of thesehave been previously recognized, namely postquantum correlations, postquantumsteering, and non-localizable channels, all of which are subsumed as specialcases of resources in our framework. Finally, we prove several fundamentalresults regarding how the type of a resource determines what conversions intoother resources are possible, and also places constraints on the resource'sability to provide an advantage in distributed tasks such as nonlocal games,semiquantum games, steering games, etc.

Postquantum common-cause channels: the resource theory of local operations and shared entanglement