I split this off a separate thread in response to a post of @Nugatory .
The matter was about the (im)possibility of transfering information using entanglement.
This is a basic thread, so I keep it simple: There are two particles/detectors, A and B. The particles are in the singlet state.

My question:
Could we claim that, should we have chosen a different detector angle for A, measurement B would have had the same outcome?
If we can't claim that, can we even rule out causation, and in that context, information transfer?
Of course any change in A doesn't affect the randomness of the outcomes of B. So, if the random pattern in B is changed in a different random pattern by changing something in A, there is no information transfer. There is an effect however (in this supposition).

My train of thought went like this: suppose a single pair in singlet state does not facilitate information transfer. However, a change in angle of A could lead to a different result in B. Then would it be conceivable that an ensemble of pairs (in time of space) would lead to a whole pattern of deviations in B as an effect of changes in the angle of detector A? I'm thinking for instance that the pattern A shows correlates with the pattern B shows (which is manifest in singlet ensembles). There is, as it were, information about a relative relation.

It may be a long shot and I'm won't be too surprised if I overlook something.

Without receiving information from A, there is no way of telling from the ensemble of B, whether B is entangled with A or not. Information from both parties is required, which is why entanglement cannot be used to send FTL information.

Entanglement can still be used to send information, such as the case with quantum super-dense coding.
Using entanglement, one can encode twice as much information on a particle than is physically possible without entanglement.
This is because manipulating A alone can change the entangled state A and B share to be any possible Bell state.
Since there are more distinguishable Bell states of a pair of particles than there are eigenstates of a single particle, one can send more information using entanglement than one can without it.

I follow that. On one side (A or B) the measurements seem random. What I am suggesting is that the actual manifestation of such a random pattern may be dependent of the angle of the detector, for if that wouldn't be the case, correlations wouldn't be able to vary between A and B dependent of the angle. A and B don't know (can't verify) that they correlate, but they do! When A and B meet each other they could say: "Hey, we correlate!" as they were doing all along. This information is relative, like it would for instance be relative to find you both have a paper with letters that combined make a message (i.e. the correlation). The information in question is as it were distributed over A and B. What I mean is that changing one of the detector angles changes the correlation, and so something has to have changed in one or both random patterns.

Let polarization be entangled(E) and be one part thru angled slit(S) and other go undisturbed(U).
If we increase time E-S can we "decrease" distance S-U?

The following is a case that outcomes at B are not affected as setting at A varies:
Trial 1.
A, α = 30^{o}
B, β = 170^{0}
In this trial θ = 140^{0} With the sin^{2} formula calculate P_{++} and P_{--} = .883
Trial 2.
A,α = 50^{0}
B,β = 170^{0}
With data outcomes from trial 1 detector A (30^{o}) and data outcomes at trial 2 detector B 170^{0} )
determine by inspection if P_{++} P_{--} also = .883
and therefore B outcomes at 170^{0} were not affected as A setting varied from 30^{0} to 50^{0}

And furthermore if the above is valid and two more trials show that A outcomes were not affected as B
setting varied. Then this could be a case for E (a,b) = ∫ dλ C (a.a' b,b' λ)

I follow that, but I am not sure I agree. If you would substitute Trial 2 (α=50°) with Trial 1 (α=30°) then Trial 2 would get a different correlation. A specific correlation occurs between two quasi random binary patterns only at certain values at a certain alignment (and I have code to back this up). If you have a pair of (quasi random) strings of values and you replace one of the pair by a different string, you most probably get a non-correlating pair (ie random p=.5).

Ok, see post #21 by @Nugatory in my thread: Local hidden variable model that equals qm predictions. The second part of reply for my sidetrack question. Unless there was a misunderstanding @Nugatory agreed with these types of substitutions being valid.

If you are suggesting taking measurements at one side of an entangled pair (say, A), and later on combine that with an independent measurement on the other side (B), I think you get two uncorrelated measurements.

Since B_{1} and B_{2} have a different dataset, replacing A_{2} with A_{1} in set 2 will affect the correlation. The set 1 correlation is characteristic for A_{1} together with B_{1}.

I am essentially in agreement with entropy1's comments on the above. Clearly the observed statistics change (a suitable set of trials) as theta changes for entangled pairs. This is not in question, is it? And if it's not, I don't follow the point either.

As to whether B outcomes are affected by varying the angle A is measured at: this is interpretation dependent. No one understands the precise mechanics.

Ok. My question primarily targeted the possibility that for a single pair, if we we would have chosen a different measurement angle for A, the outcome could have been different for B. I think this is not exactly CFD because we do measure B. There is however no verifying both of A's angles in one trail. But, as you point out, the statistics (of the combination of A and B) are dependent of the theta angle, and I observe that the theta angle can only change if one or both angles of A and B change, so when we change angle alpha there should be a change in either measurement ensemble A and/or measurement ensemble B. You could argue that if you change angle alpha, that only measurements of A change. However, that change should be in accordance with the correlation, and thus with theta, and thus A's measurements should depend on B's measurements, so then we have non-locality. Since the situation is symmetric, you could also associate the change in theta to B's measurements. So indeed we can't pinpoint the underlying mechanics. But having said that, in my view it is possible that angle alpha has 'an' effect on B's measurement outcomes.

Sure, probably so, in fact how could it not if the stats change? But again, there are interpretations in which there is no physical collapse. And in those, essentially, there may be no mutual (symmetric) collapse occurring.

Hopefully making things more definite will add clarity.

1) From B's perspective he will see ±1 with probability ½ for each no matter what A is doing. Same for A. We know if they both measure at 0º they get the same value.

2) If A measures at 45º and gets -1, while B measures at 0º and gets 1 what would they get if A measured at 0º instead? Would they both get 1? -1? If you insist that A must get 1 you are assuming she already had a value at 0º - CFD. However that experiment was not made, so we don't know.

How do you suggest in this context information might be exchanged?

Following is data set/model suggesting that for two spin 1/2 particles in superposition with spin state l Ψ > = 1/√2 [ l +,-> -l -, + > ]
Setting/outcome changes at A do not have effect on B outcomes.* While outcomes at A are independent of setting at B , outcomes at A are not independent of outcomes at B ( the correlations ) Measurement order can be A , B or B, A
A 0^{0} ..................... B 120^{0}_______________ * (sin θ/2)^{2} P--, P++ = .75 - ................................. -
+..................................-
+..................................+
-...................................-
-...................................+
+..................................+
+..................................+
+..................................+

@morrobay Your example is a perfect illustration of your quote of my text. So indeed that is a possibility. However, as I pointed out, A's outcomes must conform to theta and to B's outcomes, and hence can't be local. And my point was that since they can't be local, changes in A might just as well bring about changes in B, that being non-local too.

To clear this up: The title of my topic may be misleading - I am not advocating information transfer via entanglement, to the contrary: I am only suggesting the information in play, being the correlation between A's and B's outcomes, is dispersed (distributed), and as such dependent of A's and B's outcomes. If theta has a value of θ, the A's an B's outcomes have to 'conspire' to produce the corresponding correlation for θ. So this 'conspiration' I see as a form of 'information exchange', or perhaps better: 'information self-consistency'.

That outcomes at A and B are dependent or conform only relates to the distant correlations. This is not the same as one electron being affected by the measurement of the other

What if I propose that in your table, given θ (p=.75), on one line we flip one sign on whichever side. To keep the correlation intact, we have to flip the sign on the other side too, right?

The tables are just abreviations//averages for long stream ensembles . Can QM even address single interactions in these non classical correlations? You have to ask some of the talent here at A level going any farther with this.