Two high-energy photons are entangled and go their separate ways. One of them undergoes pair production by interacting with an atomic nucleus, and this is observed. Does the other photon also undergo pair production? Let us pretend for the moment that feasibility is no object.
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2 Answers
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No. Being entangled does not mean they mirror everything the other does. It only means certain properties are in an inseparable state. Destroying one of the pair would end this state
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$\begingroup$ So, mass is not one of those certain properties in an inseparable state, I take it. $\endgroup$ Aug 24, 2015 at 19:01
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$\begingroup$ Of course not, but electrons and positrons do. But I think you have cleared this up for me a bit Jim. When the photon goes into pair-production, it cancels its entanglement with the other photon. Is that the gist? I know when you said the photon is destroyed you didn't really mean that... $\endgroup$ Aug 24, 2015 at 19:06
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$\begingroup$ Yeah, pair production is a significant enough interaction that the entanglement is cancelled. And in some cases it's true that the photon is destroyed and a new photon is produced. $\endgroup$– JimAug 24, 2015 at 19:09
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2$\begingroup$ @Jim Are you sure it's correct to say that the entanglement is "cancelled"? I would imagine that if the photons were entangled in momentum, for example, then the momentum of the remaining photon would still be correlated with the centre-of-mass momentum of the electron-positron pair. $\endgroup$ Aug 24, 2015 at 22:06
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No. The other photon might even be forbidden to produce a pair over by itself all by itself since there might be no nucleus over by it.
The other photon doesn't have to copy what the first one does. But many things could happen to the entanglement. And that is partly because there are many ways the photons could have been entangled. For instance, you could entangle the momentums or positions of the photons in which case the pair production might act like a measurement that makes the entanglement of the photon turn into a correlation between the position or momentum of the other photon and the position or momentum of the nucleus.
Or if instead of pair producing via a nucleus you had a photon photon interaction then you could have pair A and pair B and have each one contribute one photon each to a pair production which could make an electron positron pair in a way where the remaining photons not involved become entangled with each other.
There is a sense where the entanglement is almost always just passed up a chain (like when a measurement, having the state of the measurement device become entangled with the object) or passed laterally.
