Entanglement and Regions of Space in Vacuum

[expos4ever]

TL;DR Summary

It is claimed that regions of empty space that are close to each other must be highly entangled whereas regions that are far from each other are less entangled. I want to understand why.

Sean Carroll (in a video) claims that regions of empty space (vacuum) that are near each other must be highly entangled. He appears to argue that if they were not, there would be "a lot of energy contained there" which - my conclusion - would not be consistent with these regions being low energy vacuum regions. OK, fine. What I don't get is this: Why would low entanglement between adjacent regions imply high energy?

The relevant bit is between about 53:30 and 54:30 in the following:

 

[PeterDonis]

Sean Carroll (in a video) claims that regions of empty space (vacuum) that are near each other must be highly entangled.

I don't think he's talking about quantum field theory in general. I think he's talking about a proposal of his, described in this paper:

https://arxiv.org/abs/1606.08444

And this blog post:

https://www.preposterousuniverse.com/blog/2016/07/18/space-emerging-from-quantum-mechanics/