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arXiv:2301.12081 · Physical Review Letters

Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses

Peter Bierhorst, Jitendra Prakash

Published Jun 22, 2023• 7 citations
arXivHTMLPDF

Abstract

According to recent new definitions, a multiparty behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multipartite measurement scenario (three parties, two measurement settings, and two outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources-thus witnessing the most general form of GMNL-but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device-independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.

DOI
10.1103/physrevlett.130.250201

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According to recent new definitions, a multiparty behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multipartite measurement scenario (three parties, two measurement settings, and two outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources-thus witnessing the most general form of GMNL-but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device-independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.
Quantum technologies are enjoying an unprecedented popularity, and some applications are already in the market. This thesis studies two phenomena that are behind a lot of quantum technologies: entanglement and nonlocality. We focus on multipartite systems, and ask what configurations of those systems are more useful than others. 'Usefulness' takes on different meanings depending on the context, but, roughly speaking, we aim for more entanglement or more nonlocality. Chapter 2 develops a resource theory of entanglement with a unique multipartite maximally entangled state. Chapter 3 shows that any connected network of bipartite pure entangled states is genuine multipartite nonlocal (GMNL). Chapter 4 shows that, unlike in the case of pure states, topology is crucial to determine whether networks of bipartite mixed entangled states are genuine multipartite entangled. We also obtain, to our knowledge, the first example of superactivation of GMNL. In a departure from the main ideas explored in previous chapters, Chapter 5 is devoted to developing a physical principle inspired by a seminal result in epistemics. We contend that the principle must hold for any theory of Nature and intend for it to rule out post-quantum theories which are consistent with experimentally observed results.
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.
The notion of genuinely multipartite nonlocality (GMNL) was introduced to conceptualize the fact that nonclassical resources involving more than two parties in a nontrivial way may be needed to account for some quantum correlations. In this letter, we first recall the contradictions inherent to the historical definition of GMNL. Second, we turn to one of its redefinitions, called Local-Operations-and-Shared-Randomness GMNL (LOSR-GMNL), proving that all caterpillar graph states (including linear cluster states) have this second property. Finally, we conceptualize a third, alternative definition, which we call Local-Operations-and-Neighbour-Communication GMNL (LONC-GMNL), that is adapted to situations in which short-range communication between some parties might occur. We show that linear cluster states do not have this third property, while GHZ states do. Beyond its technical content, our letter illustrates that rigorous conceptual work is needed before applying the concepts of multipartite nonlocality or entanglement to benchmark the nonclassicality of some experimentally-produced quantum systems.
The characterization of quantum correlations in terms of information-theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource. While bipartite entanglement and Bell inequality violation in this setting have been extensively studied, relatively little is known about their multipartite counterpart. In this paper, we apply and adapt the recently proposed definitions of multipartite nonlocality (Bancal et al 2013 Phys. Rev. A 88 014102) to the three- and four-partite scenarios to gain new insight on the resource aspect of multipartite nonlocal quantum correlations. Specifically, we show that reproducing certain tripartite quantum correlations requires mixtures of classical resources—be it the ability to change the groupings or the time orderings of measurements. Thus, when seen from the perspective of biseparable one-way classical signaling resources, certain tripartite quantum correlations do not admit a definite causal order. In the four-partite scenario, we obtain a superset description of the set of biseparable correlations which can be produced by allowing two groups of bipartite non-signaling resources. Quantum violation of the resulting Bell-like inequalities is investigated. As a byproduct, we obtain some new examples of device-independent witnesses for genuine four-partite entanglement, and also device-independent witnesses that allow one to infer the structure of the underlying multipartite entanglement. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
Genuine multipartite Bell nonlocality (GMNL) aims at capturing correlations between many distant observers that are globally Bell nonlocal. A commonly used definition for GMNL is based on biseparable models constructed from non-signalling correlations. Here we uncover an effect of superactivation of GMNL in this framework. Specifically, by locally wiring together two copies of a biseparable correlation, i.e. not GMNL, one can obtain another correlation that is GMNL. We show that this is possible for any number of parties, and for quantum-realizable correlations. Finally, we show that superactivation of GMNL is also possible at the single-copy level, via a catalytic protocol involving only local wirings. These results question the operational meaning of this definition of GMNL.
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.