# I (In)dependence in entanglement experiments

#### entropy1

Summary
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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#### vanhees71

Gold Member
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).

#### entropy1

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...

#### vanhees71

Gold Member
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!

#### entropy1

@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 refering 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.

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.

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