(In)dependence in entanglement experiments

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Discussion Overview

The discussion revolves around the nature of independence and correlation in entanglement experiments, particularly focusing on how measurements of entangled particle pairs relate to one another across multiple experimental runs. The scope includes theoretical considerations of quantum mechanics and the implications of entanglement on measurement outcomes.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question how independent entanglement experiments can yield correlations, suggesting that if each run is independent, the correlation should be zero.
  • Others argue that correlations exist only within each pair of entangled particles and not between different pairs, implying that the presence of correlations does not indicate dependence across runs.
  • A participant emphasizes that to test probabilistic predictions, the members of the ensemble must be independent, and any additional correlations would indicate a different state being tested.
  • One participant introduces the idea that the orientation of measurement devices (like SG magnets) can create correlations in the ensemble of measurements, suggesting a dependence based on experimental setup.
  • Another participant expresses confusion about the relationship between independence of runs and the presence of correlations, questioning if non-local information is necessary for non-zero correlations.
  • A later reply indicates a struggle to articulate these concepts clearly, leading to a withdrawal from the discussion.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the implications of independence and correlation in entanglement experiments. Multiple competing views remain about the nature of correlations and dependencies in measurements across different experimental runs.

Contextual Notes

Participants express uncertainty about the definitions of independence and correlation, as well as the implications of measurement setups on the outcomes. There are unresolved questions about the nature of information transfer between entangled particles and the conditions under which correlations manifest.

entropy1
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TL;DR
Are runs in an entanglement experiment independent or dependent?
If an entanglement experiment, whereby an entangled pair of particles is measured at both ends, is independent of the next entanglement experiment with another pair of entangled particles, how can there be a correlation? It seems that each independent run does not influence the next run, but wouldn't the correlation measured over several runs in that case not have to be zero? And if the correlation is significantly deviated from zero, does that not mean that the runs must be dependent? And what causes this dependence?
 
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The correlation is of course there only for each pair. Not for particles from a different pair, if really the two-particle entangled states are realized by the state preparation.

If there'd by correlations between the particles in different pairs, you'd not describe two-particle entangled states, but (mabye) multi-particle entangled states, which are of course as possible, but then describing a different situation (which usually is technically more difficult to realize as all the people trying to construct many-qubit quantum computers know only too well).
 
vanhees71 said:
The correlation is of course there only for each pair. Not for particles from a different pair, if really the two-particle entangled states are realized by the state preparation.

If there'd by correlations between the particles in different pairs, you'd not describe two-particle entangled states, but (mabye) multi-particle entangled states, which are of course as possible, but then describing a different situation (which usually is technically more difficult to realize as all the people trying to construct many-qubit quantum computers know only too well).
If you mean correlation between runs, that is not what I mean. A pair of entangled particles cannot yield a correlation. So I mean several runs of independent single pairs, and calculating the correlation of paired measurement outcomes, straight forward really...
 
Entanglement describes always a very strong correlation. As shown by Bell, it's stronger than in any deterministic local hidden-variable theory, which leads to the violation of the corresponding inequality derived under this assumption.

Obviously I don't understand the question then, because to test a probabilistic statement (of QT or otherwise) you have to prepare each member of the ensemble used to make the measurements independent from each other. The strong correlations describe correlation of each single pair.

E.g., in the spin-singlet state of two spins 1/2,
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|-1/2,1/2 \rangle),$$
there's a 100% correlation between these two spins, though each single spin is maximally indetermined, and that's the case for any such prepared state. To test the probabilistic predictions, you have to make sure that in repeating the experiment forming an ensemble there are NO correlations between the members of the ensemble. If there are such additional correlations you test a different state!
 
@vanhees71 So maybe we have this misunderstanding: I mean that, for instance with two SG magnets, the respective orientation of the magnets create a correlation in the ensemble of respective measurements that depends on the respective orientation of the magnets. This is the correlation I'm referring to. This is considered a dependence of the respective measurements (A and B). Further, I would say that for the correlation to be manifest, it requires an ensemble of runs.

entropy1 said:
It seems that each independent run does not influence the next run, but wouldn't the correlation measured over several runs in that case not have to be zero? And if the correlation is significantly deviated from zero, does that not mean that the runs must be dependent? And what causes this dependence?

So, if the runs (of measuring a pair) are random and independent (this is what you mean), what would cause this correlation between the respective outcomes at the magnets? Wouldn't random and independent runs only be able to produce zero correlations in the ensemble, unless there is some influence between the particles?

Said differently: if the particles only have local information at the magnets, the outcome at each magnet would be random and that would mean zero correlation between outcomes. So, conversely, if there is a non-zero correlation between the outcomes, the information in the pair would have to be non-local.

If the outcomes at each end would be random, so there is no non-locality, then we have to consider that the runs themselves have some (inter)dependence.

I have some trouble getting this communicated cleary, for which I apologize.

EDIT: Nevermind. I can't undertand myself anymore so forget it.
 
Last edited:
entropy1 said:
I can't undertand myself anymore so forget it.

Thread closed.
 

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