Could you say that two electrons in the ground state of a helium atom experience quantum entanglement? They are both in the same energy level and cannot have the same quantum numbers. If one is spin up, the other must be spin down. So, if one "flipped" spins, the other would have to also flip spins or violate sassy Pauli exclusion principle.

  • $\begingroup$ I've never seen the Pauli exclusion principle described as "sassy"! But in any case, I would say yes: the electrons in any atom are (in some sense trivially) entangled because you have to anti-symmetrize the many-electron wave function, and such a state cannot be a product state. $\endgroup$ – march Dec 14 '15 at 4:24
  • $\begingroup$ Entanglement arising from (anti-)symmetrization is a subtle issue and it depends very much on the perspective (i.e., what you call entanglement), see also the answer by Nicolai Miklin. $\endgroup$ – Norbert Schuch Dec 14 '15 at 13:47

In this context it is convenient to look at entanglement as a resource for quantum information tasks. There are several opinions about usefulness of correlations between identical particles as such a resource, but I think the most orthodox one is expressed in this review: http://arxiv.org/abs/1312.4311. The main point follows already from the title: you can extract entanglement from such correlations, but you can't use it otherwise, which means that there is no entanglement.

  • $\begingroup$ So you mean they are entangled in a way, but not in the useful way that people are interested in? Does that sum up what you mean? $\endgroup$ – Z Leach Dec 14 '15 at 23:29
  • $\begingroup$ Yes. Pretty much. Although some people (maybe most of them) prefer not to call it entanglement, it is tricky, because these correlations look like entanglement. $\endgroup$ – Nikolai Miklin Dec 15 '15 at 9:17
  • $\begingroup$ They are indeed entanglement, just not of a sort useful for QIT $\endgroup$ – Lewis Miller Dec 16 '15 at 2:40
  • $\begingroup$ Am I missing something stupid or does the cited paper say literally the opposite of what is being claimed in this answer? From the abstract: "we show that any entanglement formally appearing amongst the identical particles, including entanglement due purely to symmetrization, can be extracted into an entangled state of independent modes, which can then be applied to any task." Which seems to be clearly claiming that identical particle entanglement is a full resource for quantum information and in that sense should be considered "true" entanglement. $\endgroup$ – Rococo Apr 23 '17 at 17:45
  • $\begingroup$ See also: journals.aps.org/prb/abstract/10.1103/PhysRevB.76.113304 $\endgroup$ – Rococo Apr 23 '17 at 17:45

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