Full Network Nonlocality

Abstract

Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalization to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analyzing local and theoryindependent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input-output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum elegant joint measurements.

Recycling nonlocality in a quantum network

“…A natural next step is therefore to investigate recycling of network nonlocality based on entanglement swapping. Although such scenarios can still maintain conceptual links to standard Bell scenarios [66], there has recently been several proposals of entanglement swapping experiments that constintute more genuine notions of network nonlocality [39,67,68]. A particularly interesting prospect is to investigate unsharp implementations of joint, entangled, measurements for recycling network nonlocality.…”

Proofs of network quantum nonlocality aided by machine learning

“…[19] demonstrated that bipartite nonlocality can be "disguised" in networks, leading to network-nonlocal distributions. Examples of this phenomenon motivated the search of stronger definitions for nonlocality in networks, that are in closer relation to the network structure [20] and give a more pivotal role to entangled measurements [21].…”

“…One of the benefits of formulating the compatibility problem as a linear program is that a negative answer provides, via Farkas' lemma [29], a witness which applies to distributions other than that analyzed. In fact, this approach is standard for finding Bell inequalities from results on the inexistence of local models [20,26,30]. For the inflation used (recall Fig.…”

Entanglement swapping and quantum correlations via Elegant Joint Measurements

“…Although originally introduced in the context of collective spin measurements [21,22], they were re-introduced in order to remedy the shortcomings of the Bell state measurement in triangle-nonlocality [23] and they were subsequently found to be connected to quantum state discrimination [24]. Very recently, they have been used as the central component of both network nonlocality protocols, that bear no resemblance to standard Bell inequality violations [25], and full network nonlocality protocols, which constitute a stronger, more genuine, notion of nonlocality in networks [26]. The progress has also motivated recent experiments that realize one type of EJM on a superconducting quantum processor [27] and as a photonic quantum walk [28].…”