Mixed-state Entanglement for AdS Born-Infeld Theory

TL;DR

This paper investigates how mixed-state entanglement measures in AdS Born-Infeld theory vary with system parameters, revealing complex behaviors of holographic entanglement entropy, mutual information, and entanglement wedge cross-section, and demonstrating universality across BI-like models.

Contribution

It provides the first detailed analysis of mixed-state entanglement in AdS Born-Infeld theory, uncovering universal behaviors and analytical insights into the effects of nonlinear electromagnetic coupling.

Findings

HEE and MI vary monotonically with BI factor b

EWCS exhibits non-monotonic behavior with b

Results are universal across BI-like models

Abstract

We study the mixed-state entanglement for AdS Born-Infeld (BI) theory. We calculate the mixed-state entanglement and investigate the relationship between it and the system parameters. We find that the holographic entanglement entropy (HEE) and mutual information (MI) exhibit monotonically increasing and decreasing behavior with BI factor $b$. However, the entanglement wedge cross-section (EWCS) exhibits a very rich set of phenomena about system parameters. EWCS always increases with $b$ when $b$ is small and then monotonically decreases with $b$. These behaviors suggest that increasing the BI factor, which is essentially enhancing the coupling between the background geometry and the transport properties can always enhance the EWCS. The coupling between the entanglement and the transport behaviors has also been studied in condensed matter theories and is important to construct a stable quantum circuit. We also provide analytical understanding of the above phenomenon. Furthermore, we have tested two additional BI-like models and find the universality of these results, suggesting the crucial role of the BI term in governing the interplay between nonlinear electromagnetic effects and entanglement.