Say we start with an entangled electron--positron pair and we separate them. I w

Question

Say we start with an entangled electron--positron pair and we separate them. I want to take the entangled electron and bind it to a proton or the outer shell of an atom.

Is it possible to do this while having the entangled electron still remain entangled with the positron? Would the electromagnetic interaction with the proton "make a measurement" of the entangled electron's spin because of its magnetic field?

Assuming my above example is possible, say we then measure the spin of the positron that's far away. Whatever it may be, the entangled electron bound to the atom will now assume the opposite spin state. The total angular momentum of the atom will now be at a different value than what it was before, and therefore something must happen to conserve this, emit a photon?

Again, if my above example has a measurable effect whether it emits a photon or changes in some way, then this suggests to me that if we have an ensemble of these special atoms, we will be able to send information via quantum entanglement. By having these special atoms in one station and the entangled positrons in another station, we can measure or not measure, 1 or 0, the spin of the entangled positron and thus produce a measurable effect at the other station via the special atoms

Explanation / Answer

You say:

I want to take the entangled electron and bound it to a proton or the outer shell of an atom.

The act of binding the electron with a proton, or an outer shell of an atom, means that some energy in the form of electromagnetic radiation will be given up by the electron in order to fall in an available energy level. A photon takes away spin 1 and any mathematical relationship that your electron's spin had with the world outside the atom world is lost.

So the answer is no.

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