Usually when we talk about entanglement, we mean entangled spin states (of electrons) or polarizations (of photons). My questions are:
Does pair production guarantee the product electron and positron entangled?
If there's no observer measuring either particle, can we say the types, or charge, of the particles are also entangled, with a wavefunction like: $\frac{1}{\sqrt{2}}( |+e\rangle \pm |-e\rangle)$?
Best Answer
I've already quite a long time ago noticed that in particle physics we usually do stuff that quantum-computing people will call an "entaglement". We just don't phrase it like that, because we are used to it and we aren't much "in awe" about it.
So the "entanglement" you are talking about is long known in particle physics.
The earliest reference I know is this:
“Pion-Pion Correlations in Antiproton Annihilation Events”, Phys. Rev. Lett. 3 (1959), no. 4, 181–183.
As you see, it is for pions (charged, actually).
The more "modern" review is this:
“Bose–Einstein and Fermi–Dirac interferometry in particle physics”, Rep. Prog. Phys 66 (2003) 481.