Quantification of quantum dynamics with input-output games

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.

Section: Definition 5 For a Given Global Type T We Define A Distrimentioning

confidence: 99%

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

Schmid

Mudassar

et al. 2021

“…As such, we expect that many 'resource theories of processes' (see Ref. [14]), most of which take individual maps as resources, can be extended to encompass multi-step scenarios using our framework; this include many important recent developments in resource theories of channels [74][75][76]97]. Another completely distinct resource theoretic description of channels utilises discrimination tasks [98].…”

Section: Relation To Other Resource Theoriesmentioning

confidence: 99%

Resource theories of multi-time processes: A window into quantum non-Markovianity

Berk

Garner

Yadin

et al. 2021

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess — corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.

“…As a final remark, we recall that the semiquantum games introduced in [71] to test bipartite states in a measurement-device independent fashion [31], can be transformed into guessing games suitable for testing, always in a measurement-device independent fashion, quantum channels and quantum memories [72,73]. More generally, such single-party guessing games have found application in the context of measurement resources [72,74,75] and general convex resource theories [76][77][78][79]. We leave further investigations about relations between these works and ours for future research.…”

Section: Open Question 4 What Can Be Learned By Considering a Type-independent Framework Of Locc Nonclassicality?mentioning

confidence: 99%

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

Schmid

Rosset

Buscemi

2020

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.