Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom.It is sometimes said that Einstein discovered entanglement in 1935, and it was immediately recognized as the central defining feature of quantum mechanics. But as the above paper notes, the word was not in common use until about 1987, and did not find its way into textbooks until after that.
As the article explains, entanglement is not some peculiarity of tricky spin experiments. It is a property of all quantum systems.
Entanglement is explained as the thing that makes quantum mechanics nonlocal, and hence the essence of why the theory is non-classical and mysterious.
Quantum-mechanically, an interference pattern occurs due to quantum interference of the wavefunction of a photon. The wavefunction of a single photon only interferes with itself. Different photons (for example from different atoms) do not interfere.This is not an exact quote, but he said something similar.
This is a confusing statement, and I would not take it too literally. But in a similar spirit, I would say that a quantum particle can be entangled with itself.
Entanglement is often introduced by describing creation of a pair of particles with equal and opposite spins. But it is much more common. In any atom with several orbital electrons, those electrons are entangled. Nearby particles usually are. The case of the equal and opposite pair is interesting because that gives distant entanglement, but nearby entanglement occurs all the time.
Consider a stream of particles being fired into a double slit. Each particle is interfering with itself, and is entangled with itself. The interference results in the interference pattern on the screen.
The entanglement results in each particle hitting the screen exactly once. If you purely followed the probabilities, there are many places on the screen where the particle might hit. Those possibilities are entangled. If the particle is detected in one spot, it will not be detected in any other.
You cannot understand the experiment as localized probabilities in each spot of the screen.
Viewed this way, I am not sure the 2-particle entanglement story is any more mysterious than the 1-particle story. Maybe explanations of entanglement should just stick to the 1-particle story, as the essence of the matter.
Update: Reader Ajit suggests that I am confusing entanglement with superposition. Let me explain further. Consider the double-slit experiment with electrons being fired thru a double-slit to a screen, and the screen is divided into ten regions. Shortly before an electron hits the screen, there is an electron-possibility-thing that is about to hit each of the ten regions. Assuming locality, these electron-possibility-things cannot interact with each other. Each one causes an electron-screen detection event to be recorded, or disappears. These electron-possibility-things must be entangled, because each group of ten results in exactly one event, and the other nine disappear. There is a correlation that is hard to explain locally, as seeing what happens to one electron-possibility-thing tells you something about what will happen to the others. You might object that the double-slit phenomenon is observed classically with waves, and we don't call it entanglement. I say that when a single electron is fired, that electron is entangled with itself. The observed interference pattern is the result.