[Paper Review] Wigner's approach enabled detection of multipartite nonlocality using all different bipartitions

Sumit Nandi, Debashis Saha+2 more|arXiv (Cornell University)|Feb 23, 2022

Quantum Information and Cryptography4 citations

TL;DR

This paper introduces a generalized Wigner-type local realist (LR) inequality framework that detects multipartite nonlocality across all possible bipartitions of an N-partite quantum system. By deriving a set of individual LR inequalities for each of the (2^{N-1} - 1) distinct bipartitions, the method rigorously certifies genuine multipartite nonlocality when all inequalities are quantum-mechanically violated, enabling identification of which specific bipartition exhibits nonlocality—offering a finer characterization than prior approaches like Svetlichny’s inequality.

ABSTRACT

Distinct from Bell's approach, Wigner had 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 generalised Wigner's inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present work, this limitation has been overcome by formulating a further generalisation 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 characterisation 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 generalisation 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.

Motivation & Objective

• To overcome the limitation of existing multipartite local realist inequalities, such as Svetlichny’s, which cannot identify which specific bipartition exhibits nonlocality.
• To develop a generalized Wigner approach that formulates a distinct local realist inequality for every possible bipartition of an N-partite system.
• To rigorously certify genuine multipartite nonlocality by demonstrating quantum violations of all individual inequalities in the set, ensuring nonlocality is not reducible to correlations among fewer than N particles.
• To provide a finer characterization of nonlocality by linking each quantum violation to a specific bipartition, enabling experimental and theoretical identification of nonlocal substructures.

Proposed method

• The authors derive a set of local realist (LR) inequalities based on Wigner’s original approach, assuming joint probability distributions (JPDs) for measurement outcomes under locality.
• For each of the (2^{N-1} - 1) distinct bipartitions of an N-partite system, a separate Wigner-type LR inequality is formulated, ensuring each bipartition is analyzed independently.
• The method relies on the assumption that local realism holds for each bipartition, with quantum mechanical violations of these inequalities indicating nonlocality specific to that partition.
• The framework is tested on tripartite and quadripartite states, showing that individual quantum violations of all inequalities in the set confirm nonlocality across all bipartitions.
• The measurement settings for violating each inequality are generally different, allowing independent experimental verification across bipartitions.
• The approach is contrasted with Svetlichny’s inequality and other multipartite nonlocality criteria, highlighting its advantage in identifying the specific nonlocal bipartition.

Experimental results

Research questions

• RQ1 Can a local realist inequality framework be generalized to detect nonlocality across all possible bipartitions of a multipartite quantum state?
• RQ2 Does the quantum violation of a Wigner-type local realist inequality for a specific bipartition guarantee nonlocality specific to that partition?
• RQ3 Can the simultaneous violation of all such inequalities across all bipartitions serve as a rigorous certification of genuine multipartite nonlocality?
• RQ4 How does this Wigner-based approach differ in interpretability and experimental feasibility from Svetlichny’s inequality or other multipartite nonlocality criteria?
• RQ5 Can this method provide a finer characterization of nonlocality by identifying which specific bipartition is nonlocal, unlike previous approaches?

Key findings

• The paper successfully derives a complete set of Wigner-type local realist inequalities—one for each of the (2^{N-1} - 1) distinct bipartitions of an N-partite system.
• Quantum mechanical violations of all individual inequalities in the set provide rigorous certification of genuine multipartite nonlocality, excluding any hybrid local-nonlocal models.
• Each quantum violation is linked to a specific bipartition, enabling identification of which subsystems are nonlocally correlated, a feature absent in Svetlichny-type inequalities.
• The method is demonstrated to be effective for tripartite and quadripartite states, showing that nonlocality can be detected and characterized across all possible bipartitions.
• The measurement settings required for violating each inequality are generally different, allowing independent experimental validation of nonlocality in each bipartition.
• The framework offers a more flexible and informative characterization of nonlocality than existing approaches, particularly in identifying the precise source of nonlocal correlations within a multipartite state.