I Vacuum entanglement: between what and what, exactly?

[Husserliana97]

Hello,

I sometimes read that the entanglement of the vacuum state of a field -- maximal and ubiquitous -- is an inescapable axiom of QFT. In articles often oriented towards AQFT (like SJ Summers' one, Yet more ado about Nothing) but also in this intervention by Susskind (from 32mn30: https://www.cornell.edu/video/leonar...3-entanglement). But what exactly is this entanglement between?

As far as the video is concerned, there would be entanglement between separate regions of the same field, even if this separation were a space-like interval. These regions (Susskind calls them “cells”) would then constitute non-separable subsystems. As a result, everything contained in any one region, by which I mean all the field variables it contains, are entangled with variables contained in other regions. But can we then infer, from this entanglement (between cells, and consequently between the variables or degrees of freedom of these cells), the one suggested by Susskind, namely, an entanglement between vacuum fluctuations (or "virtual particles") ? The answer seems to me to be yes, but I'd like to be quite sure.

Especially since, in a recent article (Copenhagen vs Everett, Teleportation, and ER=EPR) [1], Susskind writes: “In the vacuum of a quantum field theory, the quantum fields in disjoint regions of space are entangled. One way to picture this is that virtual pairs of entangled particles are constantly appearing for short times”. Well, it's one thing to derive from the entanglement of regions the entanglement of their (in this case virtual) fluctuations, but to consider that one is a possible translation (“picture”) of the other is to take it one step further, it seems to me.

[1] https://arxiv.org/abs/1604.02589

[Moderator's note: post edited to remove attachment and substitute link to the arxiv page, in accordance with PF policy.]

 

[PeterDonis]

Moderator's note: Thread moved to QM interpretations subforum.

 

[Demystifier]

It's entanglement between fields at different points in space. (Any talk about virtual particles in this context is highly misleading.)

 

[Husserliana97]

Well, Susskind talks about virtual particles here.... as if the two images (entanglement between field regions and between virtual particle/antiparticle) were equivalent. Thanks in any case for your reply!

 

[martinbn]

You are asking what the entanglement is between? But the statement you quote says that the vacuum is in an entangled state. In any quantum theory the state of a system, no matter if it is particles or fields, is described by an element of a Hilbert space $\mathcal H$. If the space is a product $\mathcal H = \mathcal H_1\otimes \mathcal H_2$, then the state $\psi\in \mathcal H$ is entangled if it cannot be written as a product $\mathcal\psi_1\otimes \mathcal \psi_2$.

 

[Husserliana97]

However, the quotation refers to correlations between several "subsystems" of the field, even though they should be assigned a single global state that cannot be factorized into a product of independent states of the various subsystems.
In QM, we speak of an entangled global state, and at the same time of correlated particle times, at least with regard to a certain observable...
Or do you mean: the vacuum state is intricate if this state cannot be written as a simple product of independent states of the subsystems (which you express in terms of H decomposition) ? But my question remains: what are these subsystems? The field's modes? Its degrees of freedom? Its (vacuum) fluctuations? Or regions of space?