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arXiv:1911.12462 · Physical Review Letters

Type-Independent Characterization of Spacelike Separated Resources

Denis Rosset, David Schmid, Francesco Buscemi

Published Nov 17, 2020• 35 citations
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Abstract

Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in quantum networks. Not all such objects are useful, however. In the context of spacelike separated parties, devices which can be simulated using local operations and shared randomness are useless, and it is of paramount importance to be able to practically distinguish useful from useless quantum resources. Accordingly, a body of literature has arisen to provide tools for witnessing and quantifying the nonclassicality of objects of each specific type. In the present Letter, we provide a framework which subsumes and generalizes all of these resources, as well as the tools for witnessing and quantifying their nonclassicality.

DOI
10.1103/physrevlett.125.210402

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Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in quantum networks. Not all such objects are useful, however. In the context of spacelike separated parties, devices which can be simulated using local operations and shared randomness are useless, and it is of paramount importance to be able to practically distinguish useful from useless quantum resources. Accordingly, a body of literature has arisen to provide tools for witnessing and quantifying the nonclassicality of objects of each specific type. In the present Letter, we provide a framework which subsumes and generalizes all of these resources, as well as the tools for witnessing and quantifying their nonclassicality.
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.
When two parties, Alice and Bob, share correlated quantum systems and Alice performs local measurements, Alice's updated description of Bob's state can provide evidence of nonclassical correlations. This simple scenario, famously introduced by Einstein, Podolsky and Rosen (EPR), can be modified by allowing Bob to also have a classical or quantum system as an input. In this case, Alice updates her knowledge of the channel (rather than of a state) in Bob's lab. In this paper, we provide a unified framework for studying the nonclassicality of various such generalizations of the EPR scenario. We do so using a resource theory wherein the free operations are local operations and shared randomness (LOSR). We derive a semidefinite program for studying the pre-order of EPR resources and discover possible conversions between the latter. Moreover, we study conversions between post-quantum resources both analytically and numerically.
Quantum-entangled measurements are known to enable multi-party behaviors that are impossible with unentangled measurements on nonlocal resources, even those that are super-quantum and bound only by the no-signaling principle. This advantage can be witnessed by the entanglement swapping protocol, along with corresponding impossibility results for "nonlocality swapping". However, the advantage assumes the absence of pre-existing nonlocal resources shared by the swapped-to parties; it no longer holds if all pairs of parties are allowed to share bipartite nonlocal resources. Here, we consider a resource-theoretic perspective in which bipartite nonclassical resources are free resources that can be shared by any pair of parties in a multipartite network, and ask whether quantum entangled measurements can still provide an advantage over certain basic measurements, known as wirings, of nonsignaling nonlocal resources. We resolve this question in the affirmative by demonstrating an explicit four-party behavior that can be achieved with bipartite quantum resources subject to entangled measurements, and cannot be achieved if the bipartite resources are allowed to be more general nonsignaling nonlocal "boxes" so long as the measurements are restricted to local wirings, even also allowing for globally shared classical randomness. Furthermore, the argument generalizes: the same separation can be witnessed for K+2 parties with access to K-partite nonlocal resources for any K > 2. We also examine these results in different contexts, such as the star network configurations and scenarios not admitting globally shared classical randomness, further enhancing understanding of the capabilities of entangled measurements in multi-party configurations.
We study a strong form of genuine multipartite nonlocality (GMNL), where an nnn-partite scenario admits a quantum strategy generating outcomes belonging to a restricted set with certainty, whereas every strategy built from nonclassical resources shared among at most k<nk<nk<n parties fails this criterion with positive probability. This generalizes what is referred to as strong contextuality/nonlocality, or pseudotelepathy, beyond ruling out local models. For the simplest five-party Bell scenario of two binary-outcome measurement settings per party, we use the inflation technique to demonstrate that a game with a perfect quantum strategy witnesses a robust separation from models built from bipartite resources under local operations and shared randomness (LOSR), establishing the behavior is LOSR-GMNL. We provide broader context for this result by investigating its simulability with resources shared among three or four parties under different resource models and alternative definitions of GMNL. A central open question is whether nnn-party quantum resources can achieve such a separation from models built from (n−1)(n-1)(n−1)-party resources, for n≥3n\ge 3n≥3. We make progress here by constructing a family of robustly LOSR-GMNL games with εεε-optimal quantum strategies experimentally indistinguishable in the limit from true probability-one-winning strategies for any desired level of precision.
With the advent of device-independent quantum information processing, nonlocality is nowadays regarded as a resource that can be used for various tasks. Using the analogy of entanglement theory, we approach nonlocality from this perspective. In order to do so, we analyze in full detail the operations that can be implemented in this scenario and under which nonlocality cannot increase. This provides a theoretical basis from which to study how to order and quantify nonlocal behavior. Finally, we review several nonlocality measures and discuss their validity from this point of view. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’.