Entanglement Structure of Nonlocal Field Theories Demonstrates Volume-Law Scaling and Enhanced Multipartite Correlations

The subtle ways in which distant parts of a system become linked, known as nonlocal interactions, profoundly influence quantum entanglement, but their full impact on complex correlations remains largely unexplored. Reza Pirmoradian, from the School of Quantum Physics and Matter Institute for Research in Fundamental Sciences, and Ershad Damavand, from the Institute of Higher Education, alongside M. Hossein Bek-Khoshnevis, Sadaf Ebadi, and M. Reza Tanhayi, all from the Islamic Azad University, investigate these connections through detailed analysis of a theoretical nonlocal field. Their work reveals that the scale of nonlocality not only dictates the extent of entanglement, but also generates unexpectedly long-range correlations and a unique structure in how multiple parts of the system become linked. Importantly, the team demonstrates that increasing the distance between regions can actually strengthen their multipartite entanglement, a counterintuitive result that challenges existing holographic models of spacetime, and suggests a need for new theoretical frameworks to fully describe these complex quantum states.

This work explores a bosonic nonlocal field theory, examining correlation measures beyond entanglement entropy, namely mutual information and tripartite information. Using numerical lattice simulations, the researchers demonstrate that the nonlocality scale not only determines the onset of volume-law behaviour but also leads to striking features, including remarkably long-range mutual information and an unusual structure of tripartite information. Increasing the nonlocality scale significantly alters the quantum correlations present within the system, extending their influence over much larger distances than typically observed. These findings contribute to a more nuanced understanding of how nonlocal interactions shape quantum correlations beyond simply generating entanglement.

Non-locality and Holographic Entanglement Correspondence

This research investigates the relationship between non-locality in quantum field theories and holographic entanglement entropy. Non-locality refers to interactions that aren’t strictly local, meaning effects can propagate faster than the speed of light, or correlations exist that cannot be explained by interactions happening at a single point in spacetime. Holographic Entanglement Entropy is a powerful tool that uses the AdS/CFT correspondence to calculate the entanglement entropy of a region in a quantum field theory by calculating the area of a minimal surface in a corresponding space, providing a geometric interpretation of entanglement. The central question is how non-locality manifests itself in the holographic calculation of entanglement entropy, and whether it leads to predictable changes in the minimal surfaces used to calculate it.

The research builds on previous work demonstrating that non-local quantum field theories exhibit a volume law for entanglement entropy. The authors demonstrate that non-locality leads to significant changes in the geometry of the minimal surfaces used to calculate holographic entanglement entropy, causing them to become more diffuse compared to the sharp surfaces found in local quantum field theories. Non-locality also promotes the formation of entanglement islands, regions that contribute to the entanglement entropy even when disconnected, further contributing to the volume law behavior. The analysis extends to higher-dimensional spacetimes, showing that these features persist in more complex scenarios. The research also touches upon genuine multipartite information, which measures the entanglement between multiple regions, showing that non-locality affects this measure, indicating a more complex entanglement structure.

Nonlocality Enhances Multipartite Entanglement and Mutual Information

Scientists investigated the entanglement structure of a bosonic nonlocal field, employing numerical lattice simulations to measure entanglement entropy, mutual information, and tripartite information. Results demonstrate that the nonlocality scale governs the transition from area-law to volume-law behavior in entanglement entropy. Measurements reveal that increasing the separation between large regions can paradoxically enhance their multipartite entanglement, a surprising outcome of strong nonlocality. The team quantified mutual information, finding it remains finite even in the continuum limit, unlike entanglement entropy, due to cancellation of area-law divergences.

Further analysis focused on tripartite information, revealing a negative value, indicating genuine quantum entanglement and a monogamous correlation structure. Specifically, the field theory exhibits a monogamous entanglement pattern, where information shared between regions cannot be freely distributed. Holographic calculations successfully reproduced the volume-law scaling of entanglement entropy, validating the holographic duality. However, a significant tension emerged, as the holographic model predicted a complete suppression of both mutual and tripartite information in the volume-law phase, sharply contrasting with the rich and monogamous correlations observed in the field theory. This mismatch suggests that conventional geometric models of spacetime struggle to fully capture the complex entanglement structure of strongly nonlocal quantum states, indicating a need for new frameworks beyond geometry to accurately describe these correlations.

Nonlocality Drives Complex Multipartite Entanglement

This research demonstrates that nonlocal interactions in bosonic field theories generate complex entanglement structures beyond simple entanglement entropy measurements. Through numerical lattice simulations, scientists have shown that the scale of nonlocality dictates not only the emergence of volume-law entanglement, but also produces remarkably long-range mutual information and an unusual structure of tripartite information. Notably, increasing the separation between regions can paradoxically enhance their multipartite entanglement, revealing a highly connected system. These findings challenge conventional understandings of entanglement, as the observed correlations are more complex than those predicted by standard holographic models. While the holographic approach accurately captures the volume-law scaling of entropy, it predicts a suppression of both mutual and tripartite information, contrasting with the rich spatial correlations revealed by the field theory calculations. This discrepancy suggests that current geometric models of spacetime may be insufficient to fully describe the complex correlations arising from nonlocal interactions, indicating a need for new theoretical frameworks.