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If the universe is made of fields that exist everywhere, won’t every point in the universe become entangled with those around it, expanding out at the speed of light? How could two systems nearby one another remain unentangled?

Jeff Bass
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    Things that interact with each other generally become entangled with each other. Are you asking how we can ever justify assuming that the initial state is unentangled, given that things were already interacting with each other before then? (By the way, relativistic QFT introduces another subtlety: all physically reasonable states, including the vacuum state, are entangled with respect to location. I assume that relativistic QFT is beyond the scope of the question, but since you mention fields, I'm not sure.) – Chiral Anomaly Dec 13 '20 at 21:09
  • That sounds like a reasonable restatement. I may not fully understand my own question, but maybe I’m really wondering whether two systems can truly be 100% unentangled given that they are interacting via the field between them. Or when we say unentangled do we really mean “there is a feature of these two systems that we’ve pretty confidently determined to be independent”. – Jeff Bass Dec 13 '20 at 21:30
  • Related: https://physics.stackexchange.com/q/589696/195139 – Sandejo Dec 13 '20 at 21:48
  • @ChiralAnomaly I didn't tag you. I was hoping you could comment on my response. – Jeff Bass Dec 16 '20 at 00:40
  • @JeffBass I'm not sure if this is what you're looking for, but maybe: When an observable is measured, we project the state onto the appropriate eigenspace of the observable in order to account for our knowledge of the outcome so that we can make predictions about the next measurement. That projection can eliminate entanglement that was present (on paper) prior to the measurement, at least entanglement involving the feature that was measured. Is this related to what you're asking? – Chiral Anomaly Dec 16 '20 at 02:56
  • @ChiralAnomaly So the idea is that you "clear the entanglement" so to speak, and then keep the system isolated enough that there is minimal interaction with external influences? That makes sense to me, but is it really possible to keep a system completely isolated, or is it bound to entangle with some random field fluctuations? – Jeff Bass Dec 17 '20 at 04:40
  • @JeffBass If two quantum systems interact with each other, they typically become entangled. Are you maybe thinking of macroscopic objects that seem to remain unentangled for a long time even though they're interacting, or something like that? There is a sense in which the natural environment is constantly measuring macroscopic objects and so constantly "resetting" them to an approximately unentangled state, at least with respect to some macroscopic observables. (That phenomenon is usually called decoherence.) – Chiral Anomaly Dec 18 '20 at 00:37
  • @ChiralAnomaly I guess what I'm asking is whether it is possible to make two quantum systems NOT interact, given that they are connected by a field. – Jeff Bass Dec 20 '20 at 03:56

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If you manage to keep the entanglement contained, you can undo it. Imagine an electron in a superposition of $| \uparrow \rangle$ and $| \downarrow \rangle$ sent through a Stern-Gerlach apparatus. The spin of the electron is then entangled with its path. $$\alpha \, | \uparrow, A \rangle + \beta \, | \downarrow, B \rangle$$ If you send the electron through a second Stern-Gerlach apparatus such that the two possible paths merge into the same again, you have erased the information encoded in the position and therefore it is not entangled with the spin anymore.

In reality however, there are many uncontrolled factors which make the information leak out and therefore include more and more degrees of freedom in the entanglement. Hence, if you plan to use the superposition for an experiment you better be fast and have a way to correct for errors.

A. P.
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