Entanglement Origins

Question

Does quantum entanglement always begin with two particles in close proximity, like in the birth of virtual particle pairs for example, or can entanglement be established between two particles that are far apart? How close must particles be in order to establish an entanglement relationship?

Answer 1

The answer is "No", there is no requirement that entangled particles ever exist in a common area of spacetime, nor that they interact in any way. The protocol used to accomplish this clever trick is called Entanglement Swapping.

The basic manner of swapping entanglement is that 2 pairs of entangled photons are created independently some distance apart. These pairs are created by the usual technique of Parametric Down Conversion (PDC), and these are created together. The first entangled pair is often labeled photons 1 & 2, and the second entangled pair is labeled 3 & 4. The goal of the entanglement swap is to allow photons 2 & 3 to interact. Surprisingly, this can cause now distant photons 1 & 4 to become entangled even though they themselves didn't interact. Distance apart for photons 1 & 4 do not matter in these situations, there is no theoretical limit.

Please see Figure 1 in this 2008 paper by a team led by Anton Zeilinger (he shared the 2022 Nobel for this and other work). From the paper: "Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. ... The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication experiments as well as for novel tests on the foundations of quantum physics. ... We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4." The distance apart in this paper is quite small. But in another paper by Sun et al, the distance is much larger: photons 1 & 4 never get closer than about 25 kilometers.

Please note that Entanglement Swapping cannot be used for faster-than-light signaling. Strange but true applications of Entanglement Swapping: a) You can entangle a pair of photons after they cease to exist (delayed choice, 2012). b) You can entangle photons that have never co-existed (entanglement in time, 2012). c) You can daisy chain entanglement swaps to form a quantum repeater (2008).