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arXiv:2206.11852

Resource characterisation of quantum entanglement and nonlocality in multipartite settings

Patricia Contreras-Tejada

Published Jun 23, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2206.11852

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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.
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite entangled states are genuine multipartite nonlocal in the sense that measurements can be found on finitely many copies of any genuine multipartite entangled state to yield a genuine multipartite nonlocal behavior. Our results pave the way toward feasible manners of generating genuine multipartite nonlocality using any connected network.
Quantum mechanics is nonlocal, which makes it different from classical mechanics. Quantum information and quantum computation is a promising frontier science which is based on quantum mechanics. The nonlocality of quantum mechanics is the fundamental reason that many quantum information processing tasks have significant advantages over their classical counterparts. In this dissertation, we study three aspects of quantum nonlocality, which include the quantitative relationship between entanglement and nonlocality, the quantification of genuine tripartite nonlocality and the distribution of nonlocal quantum resources. To be specific, • We investigate the quantitative relationship between entanglement and nonlocality of bipartite quantum systems. We start by exploiting the condition that the nonlocality of two different two-qubit states can be optimally examined by a same nonlocality test setting. Via numerical simulation, we find that the nonlocality of a generic two-qubit state is upper bounded by a function of the corresponding entanglement. Further, we give an analytical proof for the upper bound and find the class of two-qubit states that can reach the upper bound. • We analyze the quantification of genuine tripartite nonlocality of a generic three-qubit state. We find a method to solve the problem for a special class of three-qubit states which include not only pure states but also mixed states. Applying the method, we drive analytical results for the genuine tripartite nonlocality of generalized GHZ states, generalized Werner states and two class of mixed states with special correlation matrices. • We investigate the distribution of nonlocal quantum resources. To distribute bipartite nonlocal quantum resources, we design an efficient quantum repeater scheme, which not only achieves the optimal transmission rate but also consumes less resources of local operations and classical communication, for the case of general pure states of two-qubit system. We also analyze the case of bipartite pure states of arbitrary dimensional quantum system and get an upper bound on the probability of a successful projection operation to produce a maximally nonlocal state. To distribute tripartite nonlocal resources, we propose a simple scenario to generate tripartite nonlocal resources from bipartite nonlocal resources. As examples, we examine the cases that two-qubit Werner states and general two-qubit pure states are prepared as resources, respectively. We get the upper bounds on the genuine tripartite nonlocality that can be generated in the scenario. We also provide the optimal measurement settings to achieve the upper bounds.
Characterizing the relation between entanglement and Bell nonlocality is a long-standing open problem, notably challenging in the multipartite case. Here we investigate the effect of superactivation of genuine multipartite nonlocality. Specifically, we show that starting from multipartite states that feature only two-party entanglement (hence almost fully separable), it is possible to obtain GMNL in the many-copy regime. This represents the weakest possible resource for GMNL superactivation. On the technical side, we develop an efficient and practical criterion for certifying GMNL superactivation based on network entangled states, as well as a perfect parallel repetition result for the Khot-Vishnoi Bell game, which are of independent interest.
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 networks are under current active investigation for the implementation of quantum communication tasks. With this motivation in mind, we study the entanglement properties of the multipartite states underlying these networks. We show that, in sharp contrast to the case of pure states, genuine multipartite entanglement is severely affected by the presence of noise depending on the network topology: the amount of connectivity determines whether genuine multipartite entanglement is robust for any system size or whether it is completely washed out under the slightest form of noise for a sufficiently large number of parties. The impossibility to obtain genuine multipartite entanglement in some networks implies some fundamental limitations for their applications. In addition, the family of states considered in this work proves very useful to find new examples of states with interesting properties. We show this by constructing states of any number of parties that display superactivation of genuine multipartite nonlocality.
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of entangled systems compared with quantum multisource networks. We prove that any symmetric entangled pure state shows stronger nonlocality than the genuinely multipartite nonlocality in the biseparable model. Similar results hold for other entangled pure states with local dimensions no larger than 333. We further provide computational conditions for witnessing the new nonlocality of noisy states. These results suggest that the present model is useful characterizing a new kind of generic quantum entanglement.