Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses

Area of Science:

• Quantum Information Science
• Quantum Networking
• Foundations of Quantum Mechanics

Background:

• Multipartite nonlocal behaviors are defined by their inability to be modeled by bipartite-only nonlocal resources.
• Recent definitions of genuinely multipartite nonlocal (GMNL) behaviors vary based on the allowance of entangled measurements or superquantum resources in underlying bipartite networks.
• Understanding GMNL is crucial for device-independent certification of quantum network effects.

Purpose of the Study:

• To categorize the hierarchy of new candidate definitions for GMNL in three-party quantum networks.
• To explore the relationship between GMNL definitions and device-independent witnesses of network effects.
• To investigate the simulation capabilities of specific multipartite behaviors within different GMNL frameworks.

Main Methods:

• Analysis of a three-party, two-measurement-setting, two-outcome scenario to identify GMNL behaviors.
• Comparison of simulation capabilities using bipartite-only networks with and without entangled measurements or superquantum resources.
• Categorization of behaviors within the established hierarchy of GMNL definitions.

Main Results:

• A specific (3,2,2) behavior is identified that demonstrates the most general form of GMNL, as it cannot be simulated without entangled bipartite measurements or superquantum resources.
• This same (3,2,2) behavior can be simulated using bipartite-only quantum states with entangled measurements, suggesting a path for device-independent certification of entangled measurements with fewer settings.
• Surprisingly, all studied behaviors, including the (3,2,2) one, can be simulated within a higher echelon of the GMNL hierarchy that permits superquantum bipartite resources while still forbidding entangled measurements.

Conclusions:

• The study establishes a hierarchy of GMNL definitions and links them to device-independent witnesses.
• A key finding challenges the theory-independent understanding of entangled measurements as distinct from bipartite nonlocality, as they can be simulated under certain GMNL definitions.
• The results highlight the complex interplay between multipartite nonlocality, bipartite resources, and entangled measurements in quantum networks.