# Pair production entanglement

Hi,

I was reading some novice stuff about quantum entanglement and I was wondering
if entanglement occurs in either of these two scenarios:

1. electron and positron entangled as a result of being created by a photon passing over a heavy nucleus

2. two free electrons entangled with each other as a result of colliding with each other

And, in general, what is the criteria for producing entangled anything.

Any help with this would be greatly appreciated! Thanks!

Ken G
Gold Member
Yes, both would produce entanglements. I don't know the formal requirement, but it seems to me that any time you have a conserved quantity that is shared between two particles, those particles will be entangled, because you can learn about the other particle by doing a measurement on one and applying the conservation law. That much could also be said classically, but the difference is that classically, we can imagine that each particle had a definite value of the quantity in question, prior to the measurement. A quantum entanglement requires that each particle be in a superposition of different definite values, but all the superpositions must satisfy the conservation law. The key thing with a superposition is that it maintains correlations that definite values can't, leading to things like Bell's theorem. A classic example is if the two particles together have a definite spin state, but each particle individually is in a superposition of different spins, and that will have entangled correlations.

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I don't know much about it myself, so I don't want to start any confusion, but I was just wondering: do two electrons have to come close before getting entangled? I would think they're entangled from the start. Am I overlooking something?

Entanglement, strictly speaking, occurs when a macroscopic object interacts with a microscopic object.

Ken G
Gold Member
I don't know much about it myself, so I don't want to start any confusion, but I was just wondering: do two electrons have to come close before getting entangled? I would think they're entangled from the start. Am I overlooking something?
From "the start" of what? Particles that are originally entangled may lose their entanglements if they interact with other things, the particles must be kept rather "pristine" to avoid destroying the entanglement. (Probably, entanglement isn't so much destroyed as diluted-- like a drop of soda in the ocean.)

Ken G
Gold Member
Entanglement, strictly speaking, occurs when a macroscopic object interacts with a microscopic object.
I don't really look at it as originating that way, why do you feel the macroscopic object is needed to have entanglement? If a photon pair creates a positron-electron pair, they will be entangled because they will have to conserve various quantities from the photons. It's true that to know the photons have those quantities, they would have needed to be measured by a macro apparatus, but the photons are still passing on the entanglement to the positron-electron without any participation by macro objects.

From "the start" of what? Particles that are originally entangled may lose their entanglements if they interact with other things, the particles must be kept rather "pristine" to avoid destroying the entanglement. (Probably, entanglement isn't so much destroyed as diluted-- like a drop of soda in the ocean.)
I'm probably wrong, but since two electrons are identical, isn't their wave function always a kind of entangled state? Entanglement means to me not being able to factorize the wave function, but that is perhaps the wrong definition?

I don't really look at it as originating that way, why do you feel the macroscopic object is needed to have entanglement? If a photon pair creates a positron-electron pair, they will be entangled because they will have to conserve various quantities from the photons. It's true that to know the photons have those quantities, they would have needed to be measured by a macro apparatus, but the photons are still passing on the entanglement to the positron-electron without any participation by macro objects.

Wasn't really trying to say entangled orginated that way. But merely saying it is a form of entanglement.

Ken G
Gold Member
Wasn't really trying to say entangled orginated that way. But merely saying it is a form of entanglement.
OK, I see, one way to do it not the only way to do it.

One of the reasons that I picked the scenario about the two electrons colliding is because I was confused as to whether or not their respective fields would cause the other's wavefunction to collapse immediately after they collide, thereby causing each one to pick its state immediately. Can somebody shed some more light on this? Thanks

Ken G
Gold Member
I'm probably wrong, but since two electrons are identical, isn't their wave function always a kind of entangled state? Entanglement means to me not being able to factorize the wave function, but that is perhaps the wrong definition?
We might wish to distinguish two types of entanglement-- one that is due to indistinguishability and comes into play when the wave functions overlap and affect each other's expectation values, and another that does not require indistinguishability or overlap of the wave functions, but affects the correlations between measurements on both particles. The latter is how the term is often used, but I wouldn't say the former isn't a form of "entanglement" because they both seem to fit the term and they are both nonclassical.

Ken G
Gold Member
One of the reasons that I picked the scenario about the two electrons colliding is because I was confused as to whether or not their respective fields would cause the other's wavefunction to collapse immediately after they collide, thereby causing each one to pick its state immediately. Can somebody shed some more light on this? Thanks
Generally speaking, interactions between quanta don't produce "collapse", that requires interaction with a macroscopic system that is too complicated for physicists to want to try and track all their internal correlations. We get away with this when the correlations are so complex they tend to cancel out in the outcomes of many repetitions of the experiment, and can be treated statistically instead. This is what is known as "decoherence," but you don't get it when just two electrons interact-- the correlations are still important there, and you have to treat the whole system.