Generating Entangled Electron Pairs

[RobbyQ]

I have read, what I believe, misleading articles about generating entangled electron pairs. Some suggesting the electron is split. But this isn't possible because it's an elementary particle with charge/mass and Spin properties. So how do we achieve generating entangled electrons with opposite spin? Or is the concept of pairing a superposition of Spin for the same electron? Or is it electron-positron pairing?

 

[PeroK]

In theory, any pair of particles can become an entangled system. Entanglement often arises from conservation laws. E.g. if a particle with zero spin decays into two particles of non-zero spin, then the spin state of the resulting particles is entangled in order to conserve the overall spin of zero.

In classical physics, the same would apply. If an object with zero momentum and zero angular momentum explodes into two pieces, then the momentum and angular momentum of each piece must be equal and opposite. That's a sort of classical entanglement.

 

[RobbyQ]

Thanks PeroK. But how would they achieve two entangled electrons one of Up spin and one with Down spin. Is it electron decay ?

 

[Nugatory]

I have read, what I believe, misleading articles about generating entangled electron pairs. Some suggesting the electron is split.

Until you tell us what you've read we can't say whether it is wrong or you misunderstood it.

Thanks PeroK. But how would they achieve two entangled electrons one of Up spin and one with Down spin. Is it electron decay ?

As well as the general principle that @PeroK mentions above (pretty much any interaction leaves the products entangled in some way) you might find https://arxiv.org/abs/1508.05949 interesting - a technique for spin-entangling two electrons.

 

[PeroK]

Thanks PeroK. But how would they achieve two entangled electrons one of Up spin and one with Down spin. Is it electron decay ?

That's not entanglement. That's two electrons each with a definite spin state. Entanglement is where the two electrons have a single (shared, as it were) spin state. This is where quantum entanglement differs fundamentally from the classical example I gave.

An electron-positron pair can arise from the decay of a neutral boson, for example.

 

[RobbyQ]

Entanglement is where the two electrons have a single (shared, as it were) spin state. This is where quantum entanglement differs fundamentally from the classical example I gave.

And is that shared spin state defined by a single wave function for the two electrons?

 

[PeroK]

And is that shared spin state defined by a single wave function for the two electrons?

Yes. Technically the mathematical characterstic that identifies it as an entangled state is that the two-electron wavefunction cannot be expressed as the product of single-electron wavefunctions. If they are not entangled, then the wavefunction can be expressed as a product of single-electron wavefunctions.