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arXiv:2202.11475 · Physical Review A

Wigner-approach-enabled detection of multipartite nonlocality using all different bipartitions

Sumit Nandi, Debashis Saha, Dipankar Home, A. S. Majumdar

Published Dec 2, 2022• 5 citations
arXivHTMLPDF

Abstract

Distinct from Bell's approach, Wigner derived a form of local realist (LR) inequality which is quantum-mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such a generalized Wigner inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present paper, this limitation has been overcome by formulating a further generalization of Wigner's approach through the derivation of a set of LR inequalities with respect to all different bipartitions of a $N$-partite system. Quantum-mechanical violations of all individual LR inequalities belonging to such a set would rigorously certify multipartite nonlocality by also providing a finer characterization of the nature of multipartite nonlocality in the following sense. The quantum-mechanical violation of any given inequality of our complete set of LR inequalities would enable identification of the corresponding bipartition which exhibits nonlocality. This is in contrast to other multipartite LR inequalities such as the Svetlichny inequality or its generalization that cannot be used to detect whether there is any particular bipartition which is nonlocally correlated. The efficacy of the scheme developed in this paper is illustrated for the tripartite and quadripartite states.

DOI
10.1103/physreva.106.062203

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Distinct from Bell's approach, Wigner derived a form of local realist (LR) inequality which is quantum-mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such a generalized Wigner inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present paper, this limitation has been overcome by formulating a further generalization of Wigner's approach through the derivation of a set of LR inequalities with respect to all different bipartitions of a NNN-partite system. Quantum-mechanical violations of all individual LR inequalities belonging to such a set would rigorously certify multipartite nonlocality by also providing a finer characterization of the nature of multipartite nonlocality in the following sense. The quantum-mechanical violation of any given inequality of our complete set of LR inequalities would enable identification of the corresponding bipartition which exhibits nonlocality. This is in contrast to other multipartite LR inequalities such as the Svetlichny inequality or its generalization that cannot be used to detect whether there is any particular bipartition which is nonlocally correlated. The efficacy of the scheme developed in this paper is illustrated for the tripartite and quadripartite states.
Nonlocal realism represents the last classical cornerstone in conflict with quantum theory, and has been shown to be largely untenable in bipartite systems [Nature 446, 871 (2007); Nature Physics 4, 681 (2008)]. We extend the Leggett-type nonlocal realistic model to arbitrary N-partite systems with polarizer settings, and derive rigorous inequalities that distinguish quantum predictions from nonlocal realistic theories. The derivation yields a fundamental double inequality that is universally valid, from which the Leggett-type bounds follow under specific measurement settings. As an illustration, we demonstrate quantum violations of these inequalities for Greenberger-Horne-Zeilinger (GHZ) states, with maximal violation 2(\sqrt{5}+1). Our results show that nonlocal realism in multipartite systems is experimentally testable.
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Abstract This paper investigates the problem of nonlocality detection for high-dimensional quantum states. To overcome the complexity of measurement settings and Bell-operator optimization in high-dimensional systems, we propose a nonlocality detection framework based on dimensional reduction and chained Bell inequalities. By employing local projection operators, arbitrary high-dimensional bipartite quantum states are mapped onto effective two-qubit subsystems. We prove that if any projected subsystem violates a chained Bell inequality, then the original high-dimensional quantum state must be nonlocal. Furthermore, the framework is generalized to multipartite quantum systems. By projecting multipartite high-dimensional states onto effective multiqubit states and applying Svetlichny inequalities, sufficient criteria for detecting genuine multipartite nonlocality are established. Our approach significantly reduces the complexity of nonlocality detection in high-dimensional systems and provides a scalable theoretical framework for studying nonlocal correlations in complex quantum systems.
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Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of postmeasurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in nnn-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems [i.e., the double-chain setting, see S. M. Cheng et al., Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.