The type-independent resource theory of local operations and shared randomness

Abstract

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

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

“…Most of our analysis and results have close analogues in Ref. [43], which undertook a similar study for the type-independent resource theory of local operations and shared randomness (LOSR), which is the appropriate resource theory for quantifying nonclassicality of common-cause processes [10] (to be contrasted with the resource theory of LOSE studied here, which is appropriate for quantifying postquantumness of common-cause processes). Both of these works are grounded conceptually in the idea that correlations should be deemed classical or nonclassical depending on what sort of causal (and inferential) theories are required to reproduce them while respecting the conservative network structure [2,10,44].…”

“…In Section 5, we recall the framework of distributed games, introduced in Ref. [43], which unifies and generalizes many traditional distributed tasks and games, including entanglement witnessing, nonlocal games, semiquantum games, steering games, teleportation games, and so on. We then discuss how players can implement type-changing LOSE operations on whatever shared resources they have access to in order to generate an optimal strategy for the game they are playing.…”

Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes

“…Using this notation, the group of LSO can be generated explicitly by the four operations which interconvert P XY |ST (x, y|s, t) with either P XY |ST (x, y|s⊕1, t), P XY |ST (x, y|s, t⊕1), P XY |ST (x⊕s, y|s, t), or P XY |ST (x, y⊕t|s, t), where ⊕ denotes summation modulo two. 23 One can readily verify [67] that the order of this group is 64.…”

“…The order of a group is the cardinality of the set of group elements, i.e., the order of the LSO group quantifies the total number of invertible LDO operations 23. A second generating set of operations for this group is given by τ 1 ,..., τ 6 defined in Proposition 16.…”

Bipartite Postquantum Steering in Generalized Scenarios

“…More generally, now that we have uncovered post-quantum steering in a bipartite setting, it paves the way for analysing a broad range of bipartite tasks from this new direction. Indeed, we note that our newly introduced Bob-with-input steering scenario has already been investigated within the context of resource theories [35].…”