Entanglement correlations, singlet spin state

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SUMMARY

The discussion centers on the measurement of entangled electrons in a singlet spin state, specifically focusing on the implications of Alice measuring the spin of one electron using the operator \hat{S}_z\otimes \hat{I}. Participants clarify that the measurement collapses the state to \uparrow\otimes\downarrow or \downarrow\otimes\uparrow, adhering to the antisymmetry of fermions. The conversation highlights that the initial state cannot project onto configurations outside of the singlet state due to the nature of quantum measurements and the properties of the operators involved.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly entanglement and measurement.
  • Familiarity with spin states and operators, specifically \hat{S}_z and the identity operator \hat{I}.
  • Knowledge of the properties of fermions and the significance of antisymmetry in quantum states.
  • Basic grasp of inner products and eigenstates in quantum mechanics.
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  • Study the implications of quantum measurement theory on entangled states.
  • Explore the mathematical framework of quantum operators, focusing on Hermitian operators and their eigenstates.
  • Investigate the concept of superposition and its role in quantum state collapse.
  • Learn about the symmetrization postulate and its application to identical particles in quantum mechanics.
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Quantum physicists, students of quantum mechanics, and anyone interested in the foundational principles of quantum entanglement and measurement theory.

  • #31
zonde said:
For two electrons to be entangled they have to originate from single place and then move to two different places by unitary evolution. So it's preservation of wave function under unitary evolution that is required as well.

I'm not sure what makes you say that ... electrons in a singlet state are always entangled, right? In fact, in atomic and molecular systems, aren't *all* of the electrons entangled with each other under normal circumstances? This entanglement appears as the exchange integral in electronic structure calculations, for example, which needs to be handled properly to get results that agree with experiment.

I guess what you were saying above applies to macroscopic entanglement experiments
like Aspect etc., but I don't think it is generally correct.
 
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  • #32
SpectraCat said:
I'm not sure what makes you say that ... electrons in a singlet state are always entangled, right? In fact, in atomic and molecular systems, aren't *all* of the electrons entangled with each other under normal circumstances? This entanglement appears as the exchange integral in electronic structure calculations, for example, which needs to be handled properly to get results that agree with experiment.

I guess what you were saying above applies to macroscopic entanglement experiments
like Aspect etc., but I don't think it is generally correct.
I do not quite understand what are your objections.
Entangled particles do not appear from nowhere at two remote places. There has to be some preparation procedure (source) of entangled pair in experiment, right?
 
  • #33
zonde: regarding the pauli exclusion principle thing, what i am saying is that i don't think the pauli explusion principle is something you should have to explicitly apply when doing analysis, it should be automatic, a consequence of the more basic rules for constructing wave functions. see, for example p204 of Griffths "Intro to QM, 2nd Ed"
 
  • #34
zonde said:
I do not quite understand what are your objections.
Entangled particles do not appear from nowhere at two remote places. There has to be some preparation procedure (source) of entangled pair in experiment, right?

Yes, I agree. My only concern was with the apparent generality of your statement:
For two electrons to be entangled they have to originate from single place and then move to two different places by unitary evolution. So it's preservation of wave function under unitary evolution that is required as well.

My point is that your statement applies to macroscopically entangled particles generated in laboratory experiments. Quantum entanglement is a much more general physical phenomenon.
 

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