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arXiv:2406.14831 · Advanced Quantum Technologies

Verifying Hierarchic Multipartite and Network Nonlocalities with a Unified Method

Ming‐Xing Luo, Shao‐Ming Fei

Published Jun 4, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite nonlocal correlations is a difficult task. A unified approach is proposed that encompasses all the quantum characteristics of the multipartite correlated system beyond from fully separable to biseparable no‐signaling correlations. A straightforward method is offered to verify general systems by lifting partial nonlocal correlations. This allows to construct a chained Bell inequality, facilitating the unified verification of hierarchic multipartite nonlocalities. The lifting method is finally applied to verify the correlations derived from quantum networks.

DOI
10.1002/qute.202400021

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Abstract The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite nonlocal correlations is a difficult task. A unified approach is proposed that encompasses all the quantum characteristics of the multipartite correlated system beyond from fully separable to biseparable no‐signaling correlations. A straightforward method is offered to verify general systems by lifting partial nonlocal correlations. This allows to construct a chained Bell inequality, facilitating the unified verification of hierarchic multipartite nonlocalities. The lifting method is finally applied to verify the correlations derived from quantum networks.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been investigated separately. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources enables the certification of the nonclassicality of all sources. In this Letter, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations that cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high-fidelity photonic quantum network by violating a single network Bell inequality.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been separately investigated. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources allows for the certification of the non-classicality of all sources. In this paper, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high fidelity photonic quantum network by violating a single network Bell inequality.
With the increased availability of quantum technological devices, it becomes more important to have tools to guarantee their correct nonclassical behavior. This is especially important for quantum networks, which constitute the platforms where multipartite cryptographic protocols will be implemented, and where guarantees of nonclassicality translate into security proofs. We derive linear and nonlinear Bell-like inequalities for networks, whose violation certifies the absence of a minimum number of classical sources in them. We do so, first, without assuming that nature is ultimately governed by quantum mechanics, providing a hierarchy interpolating between network nonlocality and full network nonlocality. Second we insert this assumption, which leads to results more amenable to certification in experiments.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
Despite the success of quantum mechanics in predicting the outcomes of experiments in many branches of physics, the foundations of the theory have remained subject of research and dispute. At the basis of this struggle with the theory lie the phenomena of nonlocality and entanglement. Since it was first predicted by Bell in 1964, nonlocality was not only verified in numerous experiments, but also identified as a useful resource for quantum information processing. Thus, the study of nonlocality is important both from a fundamental point of view and with respect to new applications in quantum information theory, such as secure cryptography and randomness generation. The identification of entanglement as a resource for quantum information led to a strong theoretical effort devoted to its characterisation and detection. Many of the resulting mathematical tools find application in several domains of physics. Although the only known way to create nonlocal correlations is to measure entangled quantum systems, it has been shown that entanglement and nonlocality constitute two inequivalent properties. Therefore, in the light of the success of entanglement theory, it is of interest to also devise a resource theory of nonlocality. The task of this thesis is to develop such a theoretical framework for the characterisation of nonlocality as a resource. To gain a better understanding of nonlocal correlations it will be necessary to investigate correlation scenarios that go beyond the situation originally considered by Bell. In doing so, this thesis provides new description of nonlocality that also have implications for the characterisation of quantum correlations and the detection of new forms of nonlocality. The first question we address is how nonlocality can consistently be defined in a scenario of arbitrarily many parties that may collaborate among each other. To this end we recognise which are the allowed physical operations in this situation and then define nonlocality as the resource that cannot be created by these operations. Our approach shows that the conventional definition of multipartite nonlocality, adopted by the community so far, is inconsistent with this operational definition; we further propose and analyse new models that do not suffer from these inconsistencies. Furthermore, we show that our findings have implications for the characterisation of quantum correlations. A recent approach to describe the set of quantum correlation consists in using principles inspired from information theory. By using a special instance of the models we defined earlier we show a fundamental limitation of this approach: no bipartite information principle is sufficient to single out the set of quantum correlations from the set of nonsignalling correlations. We then developed a description of nonlocality in an even more generalised scenario of several parties. Motivated by a result of Popescu we study scenarios where the parties are allowed to perform not only a single but sequences of measurements on their systems. Characterising nonlocality also in this scenario in operational terms and defining local models compatible with this definition, we show that a new form of nonlocality can be detected Lastly, we examine the problem of detecting the presence of nonlocality in a multipartite scenario when one is given only partial access to the global system. We find that one can verify that the total system must display nonlocality, even though the accessible subsystems only exhibit local correlations.
Abstract Nonlocality is a key feature of quantum networks and is being studied for its potential applications in quantum communication and computing. Understanding and harnessing nonlocality in quantum networks can lead to the development of faster and more secure communication systems. All the nonclassicalities are limited to discrete variable quantum networks. The first method is proposed to verify the network nonlocality of all optical quantum network consisting of two entangled states where one‐way classical communication is allowed. This provides the first device‐independent method to verify the quantum correlations generated from all optical continuous‐variable quantum networks.