Why we cannot transfer information using a spin entangled singlet?

Question

In QM and QE effects an entangled particle pair is called also a singlet with some properties of the two particles like spin, non-locally correlated. However, there is no transfer of information possible (i.e. non-communication theorem) therefore SR is not violated by this quantum effect. This is instantaneous-action-at-a-distance without involving information transfer (i.e. signalling) established theory says and could be also kinda of non-measurable with today's apparatus superluminal action IMO.

So, why exactly we cannot use for example spin entangled pairs to transfer say bit logic information instantaneously? My search revealed for especially for the case of spin, when Bob changes the polarization of the external homogeneous magnetic field B engulfing his entangled particle say for making B field spin up, then the individual spin of the particle can end up being parallel to B thus spin up but also with equal possibility end up being antiparallel spin down during the measurement. The same goes for Alice on the far other end. If she polarizes say her external magnetic field B to be say spin up in order to make the measurement and finds that her entangled particle is spin down then with 100% confidence she can say that Bob's particle at the same time is measured to be spin up. And here is actually where the whole story ends.

Not being able to actually control the individual spin of the entangled particles and therefore not having a common reference, makes transfer of information from both sides impossible and therefore both Alice and Bob end up receiving random noise.

Is my above physical description correct or did I misunderstood something?

And if yes, the above description is correct then is it logical to prohibit that possibly there is indeed some signalling (i.e. transfer of information) involved between the two particles but the non-communication theorem describes only our inability to resolve this signal due to the fact that we cannot actually control the spin probability of the entangled particles?

Therefore, as a conclusion the probabilistic nature of QM should not be attributed to the particles but to the observer's measurement? And therefore the measurement problem.

Thank you in advance for your answers.

Answer 1

There are a number of issues with your description of entanglement, including the question title. You acknowledge that FTL (nonlocal) communication is not feasible using entanglement, and even supply some explanation as to why it is not feasible. So that's good. And I will bypass a variety of quibbles to get to what I believe is your essential question:

While observers cannot extract a signal from a pair of entangled particles as of today, is there still some underlying communication occurring between the particles?

Since no one knows the precise mechanism of how nature pulls off the effects we see in entanglement, the answer is: maybe. However: There have been many extremely sophisticated experiments performed in the past 25 years or so, and their results make it exceedingly difficult to model such "hidden" communication in a matter that would still allow it to be called "communication". A better term might be "mutual rapport", but even this is questionable. There really aren't good words to describe the effect in conventional terms.

First, it is well known that the order of measurements does not affect the observed outcomes. Second, it is well known that the entangled particles can originate from independent sources far from each other.* It is less well known that the decision to entangle those 2 particles can be made remotely, in such a manner that neither of the entangled particles share any common past light cone.*

Also less known: Those particles can be entangled AFTER they are detected. And in fact they never even need to co-exist at the same time at any point in their existence.* Since detection order doesn't matter with entangled particles A and B, there is actually no evidence whatsoever that detection of A before the detection of B causes A to affect B than there is that the later detection of B affects A.

In other words: causality is only present by assumption. There is no quantum theoretical reason for A to cause something to happen to B more than vice versa. And there is certainly no experimental evidence either way. Some people believe that relativistic considerations should be brought into play, but it is far from clear that application of either SR or GR would resolve anything.

So again: the answer is a possible "maybe" and not much more. Also: there are a number of so-called interpretations of QM that attempt to answer this question and/or provide possible mechanisms. But none of these are currently generally accepted.

*Here are references if you want to know more about some of amazing experiments that give insight on this subject:

Entanglement Between Photons that have Never Coexisted The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime.

One of the authors of the next 2 papers won the 2022 Nobel for this and other work on entanglement:

Experimental delayed-choice entanglement swapping

High-fidelity entanglement swapping with fully independent sources

Answer 2

In quantum mechanics, the information you can get from a system is given by the expectation values of its observables. If you have two spatially separated systems $S_1$ and $S_2$, the expectation values of observables on $S_1$ don't depend on what happens to $S_2$ and vice versa. The expectation values of products of $S_1$ observables with $S_2$ observables does depend on what happens to each of those systems when there is entanglement. Getting those products requires measuring both systems and comparing the results so there is no prospect of using this to send information faster than light.

For reasons that are somewhat unclear there is a controversy about what is happening in reality to produce those correlations. The standard answer is some unclear waffle about non-locality that gives no explanation of the mechanism of that non-locality and has unsurprisingly led to a lot of confusion even about whether quantum theory is compatible with relativity despite the existence of many relativistic quantum field theories that make correct experimental predictions such as QED.

If you use the equations of motion of quantum theory to work out what is happening instead of waffling, then you find that locally inacessible quantum information that produce the correlations is carried in decoherent channels:

https://arxiv.org/abs/quant-ph/9906007

Explaining quantum mechanical experiments using quantum theory's equations of motion is very controversial and is commonly called the many worlds interpretation of quantum mechanics.