Bound entanglement in thermalized states and black hole radiation

TL;DR

This paper explores the complex entanglement structures in thermalized quantum systems and black hole radiation, revealing regimes of bound entanglement and early quantum correlations in Hawking radiation.

Contribution

It introduces an equilibrium approximation to analyze entanglement phases, highlighting the existence of bound entanglement in thermal states and black hole radiation.

Findings

Identification of a regime with extensive negativity but sub-extensive mutual information

Discovery of bound entanglement in thermalized states at finite temperature

Evidence of quantum entanglement in Hawking radiation before the Page time

Abstract

We study the mixed-state entanglement structure of chaotic quantum many-body systems at late times using the recently developed $\textit{equilibrium approximation}$. A rich entanglement phase diagram emerges when we generalize this technique to evaluate the logarithmic negativity for various universality classes of macroscopically thermalized states. Unlike in the infinite temperature case, when we impose energy constraints at finite temperature, the phase diagrams for the logarithmic negativity and the mutual information become distinct. In particular, we identify a regime where the negativity is extensive but the mutual information is sub-extensive, indicating a large amount of $\textit{bound entanglement}$. When applied to evaporating black holes, these results imply that there is quantum entanglement within the Hawking radiation long before the Page time, although this entanglement may not be distillable into EPR pairs.