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Scientific Reports

Experimental test of genuine multipartite nonlocality under the no-signalling principle

Chao Zhang, Chengjie Zhang, Yun‐Feng Huang, Zhibo Hou, Bi‐Heng Liu, Chuan‐Feng Li, Guang‐Can Guo

Published Dec 20, 2016• 15 citations
Publisher

Abstract

Abstract Genuine multipartite nonlocality (GMN) has been recognized as the strongest form of multipartite quantum correlation. However, there exist states that cannot violate the Svetlichny inequality derived from the standard definition of GMN, even though they possess GMN properties. The reason is that the standard definition of GMN allows correlations that permit signalling among parties, which is inconsistent with an operational definition. Here, for the first time, we present an experimental test of GMN in the no-signalling scenario, with a three-photon pure state |ψs〉 and a noisy W state. The experimental results show that these states cannot violate the Svetlichny inequality. However, our results also demonstrate that they do violate a new inequality derived from the definition of GMN based on the no-signalling principle, i.e., these states can exhibit GMN under the requirement of no-signalling. Our results will be useful for the study and applications of GMN in quantum communications and quantum computation.

DOI
10.1038/srep39327

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Abstract Genuine multipartite nonlocality (GMN) has been recognized as the strongest form of multipartite quantum correlation. However, there exist states that cannot violate the Svetlichny inequality derived from the standard definition of GMN, even though they possess GMN properties. The reason is that the standard definition of GMN allows correlations that permit signalling among parties, which is inconsistent with an operational definition. Here, for the first time, we present an experimental test of GMN in the no-signalling scenario, with a three-photon pure state |ψs〉 and a noisy W state. The experimental results show that these states cannot violate the Svetlichny inequality. However, our results also demonstrate that they do violate a new inequality derived from the definition of GMN based on the no-signalling principle, i.e., these states can exhibit GMN under the requirement of no-signalling. Our results will be useful for the study and applications of GMN in quantum communications and quantum computation.
The generation and verification of genuine multipartite nonlocality (GMN) is of central interest for both fundamental research and quantum technological applications, such as quantum privacy. To demonstrate GMN in measurement data, the statistics are commonly postselected by neglecting undesired data. Until now, valid postselection strategies have been restricted to local postselection. A general postselection that is decided after communication between parties can mimic nonlocality, even though the complete data are local. Here, we establish conditions under which GMN is demonstrable even if observations are postselected collectively. Intriguingly, certain postselection strategies that require communication among several parties still offer a demonstration of GMN shared between all parties. The results are derived using the causal structure of the experiment and the no-signaling condition imposed by relativity. Finally, we apply our results to show that genuine three-partite nonlocality can be created with independent particle sources.
Multipartite quantum nonlocality is an important diagnostic tool and resource for both researches in fundamental quantum mechanics and applications in quantum information protocols. Shared reference frames among all parties are usually required for experimentally observing quantum nonlocality, which is not possible in many circumstances. Previous results have shown violations of bipartite Bell inequalities with approaching unit probability, without shared reference frames. Here we experimentally demonstrate genuine multipartite quantum nonlocality without shared reference frames, using the Svetlichny inequality. A significant violation probability of 0.58 is observed with a high-fidelity three-photon Greenberger-Horne-Zeilinger state. Furthermore, when there is one shared axis among all the parties, which is the usual case in fiber-optic or earth-satellite links, the experimental results demonstrate the genuine three-partite nonlocality with certainty. Our experiment will be helpful for applications in multipartite quantum communication protocols.
In a multipartite setting, it is possible to distinguish quantum states that are genuinely nnn-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely nnn-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of nnn-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of three-way nonlocality. Numerical evidence suggests that all three-way entangled pure quantum states can produce three-way nonlocal correlations.
Abstract We propose an optimal and efficient numerical test for witnessing genuine multipartite nonlocality based on a geometric approach. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal models. While our knowledge concerning these models is well established for Bell-type scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine n-way nonlocal correlations for various states of three qubits and qutrits. Apart from the fundamental problem of characterizing genuine multipartite nonlocal correlations, the extension of the number of measurements beyond two is also of practical importance. As a measure of nonlocality, we use the probability of violation of local realism under randomly sampled observables, and the strength of nonlocality, described by the resistance to white noise admixture. In particular, we analyze to what extent the Bell-type scenario involving two measurement settings can be used to certify genuine n-way nonlocal correlations generated for more general models. In addition, we propose a simple procedure to detect such nonlocal correlations for randomly chosen settings with an efficiency of up to 100%. Due to its near-perfect efficiency, our method may open new possibilities in device-independent quantum cryptography applications where strong nonlocality between all partners is required.
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.
In this Letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all nonsignaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the nonsignaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any nonsignaling local models; i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit (n≥3) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.