Abstract
We define the type-independent resource theory of local operations and shared entanglement (LOSE). This allows us to formally quantify postquantumness in common-cause scenarios such as the Bell scenario. Any nonsignaling bipartite quantum channel which cannot be generated by LOSE operations requires a postquantum common cause to generate, and constitutes a valuable resource. Our framework allows LOSE operations that arbitrarily transform between different types of resources, which in turn allows us to undertake a systematic study of the different manifestations of postquantum common causes. Only three of these have been previously recognized, namely postquantum correlations, postquantum steering, and non-localizable channels, all of which are subsumed as special cases of resources in our framework. Finally, we prove several fundamental results regarding how the type of a resource determines what conversions into other resources are possible, and also places constraints on the resource's ability to provide an advantage in distributed tasks such as nonlocal games, semiquantum games, steering games, etc.
Highlights
In space-like separated experiments, it is wellknown that quantum theory can generate correlations which violate Bell inequalities [1], witnessing the fact that they cannot be explained by a classical common-cause process [2]
More general types of postquantum resources1 have been studied in a few previous works [11,12,13,14,15], which found instances of channels which cannot be generated by local operations and shared entanglement (LOSE) [16]
We have presented the type-independent resource theory of local operations and shared entanglement, or LOSE operations
Summary
In space-like separated experiments, it is wellknown that quantum theory can generate correlations which violate Bell inequalities [1], witnessing the fact that they cannot be explained by a classical common-cause process [2]. [17] noted that all logically possible bipartite quantum steering assemblages can be generated using local operations and shared entanglement, and that postquantum common causes do not give an advantage for steering of quantum states This motivated the study of multipartite postquantum steering [14, 17, 18]. We introduce a unified framework for the study of postquantum common cause channels, which subsumes all of these types of resources as special cases This framework is the resource theory [19] of local operations and shared entanglement. By considering transformations between resources that can be enacted using LOSE operations, one can quantitatively characterize the postquantumness of any given resource The study of such postquantum resources sheds light on the space of logically conceivable processes which are not realizable with quantum common causes. There are five types of nontrivial bipartite resources that have not (to our knowledge) been previously studied, namely QC→CQ, CQ→QQ, IQ→QQ, QQ→CQ, and CI→QQ
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