Can entanglement be produced from existing electrons, not from fresh pair production? Electron-positron spins created due to pair production from photons are automatically required to have opposite spins to conserve total spin in the system.
Is there theoretically a method to entangle two existing particles to have opposite spin to each other?
 A: It is possible to entangle two existing electrons. This is called quantum teleportation.
Suppose we have an electron A which has a previously measured spin of UP. We want to send this spin state information to the moon.
We create an entangled electron pair, keep one twin with us, and send the entangled twin to the moon.
Measuring the electron helf-twin will give random result, and the moon half-twin will display the opposite random result, so it is of no use in transmitting information.
We might instead measure only if our A electron and the half-twin electron combined have the same or different parity. This does not measure the entangled twin explicitly yet, thus the spin states of the entangled twin remain in superposition.
We then communicate this same or different result to the moon technician.
The moon technician measures his half-twin of the electron. If our earth result is same, then he inverts the measured result on the moon and gets the original spin state information we wanted to send over.
If our earth result is different, then the moon technician does not invert the measured result on the moon, and still gets the original spin state information we wanted to send over.
