Where does a quantum experiment *begin*?

[vanhees71]

Now it becomes totally bizzare. If the collapse is not caused by the interaction between the measured system and the measurement device, by what is it caused then?

 

[atyy]

Now it becomes totally bizzare. If the collapse is not caused by the interaction between the measured system and the measurement device, by what is it caused then?

The minimal interpretation is agnostic about "cause". "Local interactions" are properties of Hamiltonians. The collapse does not even affect the Hamiltonian, so how can the collapse be related to interactions?

 

[ddd123]

On my part, I don't know what to think. On one hand, the long-range correlations are there because of measurement, and avoiding collapse doesn't practically account for compound measurements (you have to believe it would work if you could do the practically impossible calculation of treating the whole measurement device quantum mechanically). On the other hand, collapse is frame-dependent, although the consequences are the same whatever frame you choose in the end, so it seems to beg for a deeper explanation.

 

[rubi]

That seems to be an important paper. Can we call it an interpretation of QM?

I wouldn't say it's important, since it just makes precise what was already consensus (QM is compatible with locality). However, I like it a lot, since it forces locality deniers to point out an error in the proof, which of course doesn't exist. I also wouldn't call it an interpretation. All interpretations of QM must predict the same probabilities and that papers just shows that they can arise from a classical probabilistic model that happens to be local.

My claim is at the physics level of rigour - in the same way that QED is said to be compatible with relativity. In fact, my claim is found in the standard textbooks.

I'm not asking for a mathematically rigorous presentation. Also a physicist understands compatibility with relativity to mean the implementation of the Poincare group, possibly at a non-rigorous level (as in QCD). I would already be satisfied if you could show me a non-rigorous implementation of the Poincare group that includes collapse. Show me one textbook that explicitly claims that collapse is compatible with relativity.

You are just telling me that I'm wrong, but you don't counter my arguments. Why don't you respond to the questions I posed earlier?

(By the way, I'm not even denying compatibility. I'm just saying that there is no evidence for it, but rather arguments against it.)

It's you that it is not accepting standard science.

The overwhelming majority of physicists interprets Bell's result in favour of locality and in disfavour of hidden variables. Only a die-hard minority of Bohmians advocates non-locality. Both groups agree that Bell can be interpreted in both ways. Moreover, the paper that I quoted proves unambiguously that QM is at least compatible with locality. So my view is in accordance with standard science.

 

[ddd123]

Rubi, why do you say "classical probabilistic model that happens to be local", when the abstract of the paper says "violation of Bell's inequality implies the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena"?

 

[rubi]

Rubi, why do you say "classical probabilistic model that happens to be local", when the abstract of the paper says "violation of Bell's inequality implies the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena"?

If you read the paper, you will see that he says that quantum probabilities can be interpreted as conditional probabilities that are embedded in a classical Kolmogorov model. They cannot be interpreted as absolute probabilities. However, the classical model, in which the quantum probabilities are embedded, is fully local. All of that is contained in section 8 of the paper. (In analogy to the situation in geometry: There exist non-Euclidean geometries, but they can be embedded in higher dimensional Euclidean spaces).

 

[atyy]

Show me one textbook that explicitly claims that collapse is compatible with relativity.

Weinberg.

 

[rubi]

Weinberg.

Ok. where does he claim it?

(I note that you refuse to address my questions.)

 

[atyy]

Ok. where does he claim it?

(I note that you refuse to address my questions.)

He states the axioms for QM in his QFT book, and that includes collapse. The axioms for QM carry through to QFT.

 

[atyy]

@rubi, also you can look up the literature yourself. It is absolutely standard.

 

[atyy]

For example, Peres uses the collapse in his discussion of relativistic QM.

 

[rubi]

He states the axioms for QM in his QFT book, and that includes collapse. The axioms for QM carry through to QFT.

In his QFT book, he only states the Born rule. The collapse isn't even mentioned in the list of axioms. As stevendaryl wrote earlier: The Born rule is not the same thing as collapse. Moreover, I have asked for an explicit statement that the collapse is compatible with relativity, not just a statement of the collapse.

But please respond to the following question: How can the non-commutativity of collapse be compatible with relativity, when in relativity, two time evolutions always commute?

@rubi, also you can look up the literature yourself. It is absolutely standard.

I pretty much know all the literature and I'm not aware of a single book that explains the compatibility of collapse with the Poincare group. That's why I'm asking. Your first attempt apparently failed already.

 

[atyy]

http://arxiv.org/abs/quant-ph/9906034

 

[atyy]

In his QFT book, he only states the Born rule. The collapse isn't even mentioned in the list of axioms. As stevendaryl wrote earlier: The Born rule is not the same thing as collapse. Moreover, I have asked for an explicit statement that the collapse is compatible with relativity, not just a statement of the collapse.

But please respond to the following question: How can the non-commutativity of collapse be compatible with relativity, when in relativity, two time evolutions always commute?I pretty much know all the literature and I'm not aware of a single book that explains the compatibility of collapse with the Poincare group. That's why I'm asking. Your first attempt apparently failed already.

I did not attempt to answer your question, as I said, I don't know where that is shown. But certainly collapse is standard in QM, and in all special cases studied, it is consistent with relativity. So yes, it is absolutely standard to say that collapse is consistent with relativity at the physics level of rigour.

And no, you are wrong - the Weinberg book does state collapse.

See the post above for relevant literature.

BTW, I did once see a paper addressing the question you ask, but can't remember where it is - in the meantime, see the Peres paper above.

 

[ddd123]

For example, Peres uses the collapse in his discussion of relativistic QM.

If you mean his quantum theory book, he only uses collapse for a reductio, to criticize the idea that at each instant an EPR pair has a definite wave function.

 

[atyy]

If you mean his quantum theory book, he only uses collapse for a reductio, to criticize the idea that at each instant an EPR pair has a definite wave function.

Yes, that's right. I love Peres's book, but it is deeply flawed. However in this article, he takes a more standard position: http://arxiv.org/abs/quant-ph/9906034

 

[ddd123]

Yes, that's right. I love Peres's book, but it is deeply flawed. However in this article, he takes a more standard position: http://arxiv.org/abs/quant-ph/9906034

Do you think that reductio is flawed, and if so, why?

 

[atyy]

Do you think that reductio is flawed, and if so, why?

I can't remember that part exactly. My main problem with the book is that he seems to say that coarse graining a larger system (including the apparatus) will solve the measurement problem.

 

[rubi]

I did not attempt to answer your question, as I said, I don't know where that is shown. But certainly collapse is standard in QM, and in all special cases studied, it is consistent with relativity. So yes, it is absolutely standard to say that collapse is consistent with relativity at the physics level of rigour.

It may be compatible with relativistic causality, but saying that it is compatible with relativity is different. A relativistic theory must implement the Poincare group and time evolution is just one special Poincare transformation. I think this is a consensus definition of a relativistic theory among physicists. If collapse is a form of time evolution, then it must be a Poincare transformation. This is a deeply physical requirement and not just unnecessary rigor. Physicists do care about this. Weinberg's QFT book for example puts a lot of emphasis on the implementation of the Poincare group, even though it is not a rigorous text. However, it doesn't address the issue, whether collapse is a Poincare transformation or not. I'm not aware of any physics textbook that addresses this issue.

And no, you are wrong - the Weinberg book does state collapse.

My edition of Weinberg's book "The Quantum Theory of Fields, Vol. 1" makes no mention of the collapse postulate. It just states the Born rule and nothing more. I even interpret this omission to be deliberate.

See the post above for relevant literature.

BTW, I did once see a paper addressing the question you ask, but can't remember where it is - in the meantime, see the Peres paper above.

The paper just explains the compatibility with relativistic causality. I know that this works, but it doesn't address the issue of the compatibility with the Poincare group. This is not an instance of the mathematicians/physicists battle about the right amount of rigor in physical theories. Anyway, I would be really interested in the paper you mentioned. As I said, I don't claim that collapse is incompatible with relativity. I'm just saying your arguments don't guarantee compatibility.

 

[ShayanJ]

It may be compatible with relativistic causality, but saying that it is compatible with relativity is different. A relativistic theory must implement the Poincare group and time evolution is just one special Poincare transformation. I think this is a consensus definition of a relativistic theory among physicists. If collapse is a form of time evolution, then it must be a Poincare transformation. This is a deeply physical requirement and not just unnecessary rigor. Physicists do care about this. Weinberg's QFT book for example puts a lot of emphasis on the implementation of the Poincare group, even though it is not a rigorous text. However, it doesn't address the issue, whether collapse is a Poincare transformation or not. I'm not aware of any physics textbook that addresses this issue.My edition of Weinberg's book "The Quantum Theory of Fields, Vol. 1" makes no mention of the collapse postulate. It just states the Born rule and nothing more. I even interpret this omission to be deliberate.The paper just explains the compatibility with relativistic causality. I know that this works, but it doesn't address the issue of the compatibility with the Poincare group. This is not an instance of the mathematicians/physicists battle about the right amount of rigor in physical theories. Anyway, I would be really interested in the paper you mentioned. As I said, I don't claim that collapse is incompatible with relativity. I'm just saying your arguments don't guarantee compatibility.

There is a problem with your request and I don't know why atyy doesn't point it out!
Collapse is not supposed to be a time evolution in the same sense as the unitary evolution you're talking about. Its not supposed to be a fundamental evolution besides the unitary evolution. Its not even supposed to be in a fundamental theory!
The crucial point was clearly explained by @stevendaryl but looks like it was ignored. When considering an open quantum system, an effective evolution seems to emerge for the (open) system. We're still unable to completely derive this effective evolution from the fundamental unitary evolution of the larger closed system. That's why we just consider its input and output and treat it as a blackbox and call it by such a mysterious name as collapse. When this blackbox is explained, we all expect to retain the unitary evolution that is compatible with Poincare group. So even if there is an incompatibility with the Poincare group, its because we're considering an effective evolution and ignoring part of the system.
Now it seems to me that the only point of disagreement here, can be whether that effective evolution actually emerges or not.

 

[rubi]

There is a problem with your request and I don't know why atyy doesn't point it out!
Collapse is not supposed to be a time evolution in the same sense as the unitary evolution you're talking about. Its not supposed to be a fundamental evolution besides the unitary evolution. Its not even supposed to be in a fundamental theory!
The crucial point was clearly explained by @stevendaryl but looks like it was ignored. When considering an open quantum system, an effective evolution seems to emerge for the (open) system. We're still unable to completely derive this effective evolution from the fundamental unitary evolution of the larger closed system. That's why we just consider its input and output and treat it as a blackbox and call it by such a mysterious name as collapse. When this blackbox is explained, we all expect to retain all the unitary evolution that is compatible with Poincare group.

I agree fully with this view. Collapse is an effective process that arises from a fully Poincare invariant theory with only unitary evolution. But that only means that the collapse is not part of a fundamental relativistic theory, but rather emerges from such a theory! Think of the following analogy: The quantum harmonic oscillator $H=p^2+q^2$ is not Galilei invariant, but we can embedd it into a larger theory $H=P^2 + p^2 + (Q-q)^2$ which is fully Galilei invariant. The QHO just emerges as the center of mass part of this larger system. In the same way, a theory with collapse emerges from a larger theory without collapse, in which only Poincare transformations are allowed.

I think atyy doesn't point this out, because he doesn't agree that collapse can emerge from a larger theory.

 

[ShayanJ]

I think atyy doesn't point this out, because he doesn't agree that collapse can emerge from a larger theory.

I'm not sure what you mean by a larger theory, but I expect that collapse emerges from the same QM we already have, when applied to an open system.

 

[rubi]

I'm not sure what you mean by a larger theory, but I expect that collapse emerges from the same QM we already have, when applied to an open system.

Yes, that's what I mean too. However, this is a controversial topic. Many physicists (like me) believe that this works out and others don't. I'd say the issue isn't settled completely.

 

[atyy]

It may be compatible with relativistic causality, but saying that it is compatible with relativity is different. A relativistic theory must implement the Poincare group and time evolution is just one special Poincare transformation. I think this is a consensus definition of a relativistic theory among physicists. If collapse is a form of time evolution, then it must be a Poincare transformation. This is a deeply physical requirement and not just unnecessary rigor. Physicists do care about this. Weinberg's QFT book for example puts a lot of emphasis on the implementation of the Poincare group, even though it is not a rigorous text. However, it doesn't address the issue, whether collapse is a Poincare transformation or not. I'm not aware of any physics textbook that addresses this issue.

In fact it must be, so I am not dismissing your question. It is true that is you read the standard texts, you may come to the erroneous view that the standard QFT Poincare group discussion is sufficient, when in fact it is not, since that only guarantees classical relativistic causality. In fact there is a gap in reasoning which you mention, that is, the standard discussion does not address how Poincare invariance fits with collapse. The usual assumption is that it does, because of the many special cases that have been worked out.

My edition of Weinberg's book "The Quantum Theory of Fields, Vol. 1" makes no mention of the collapse postulate. It just states the Born rule and nothing more. I even interpret this omission to be deliberate.

Weinberg gives a version of the Born rule from an old tradition in which collapse is stated as part of the Born rule.

Also, it is standard in Bell tests discussions throughout to assume collapse. In that case the theory is free relativistic QFT.

The paper just explains the compatibility with relativistic causality. I know that this works, but it doesn't address the issue of the compatibility with the Poincare group. This is not an instance of the mathematicians/physicists battle about the right amount of rigor in physical theories. Anyway, I would be really interested in the paper you mentioned. As I said, I don't claim that collapse is incompatible with relativity. I'm just saying your arguments don't guarantee compatibility.

In fact there is not much battle - most physicists would love to see a rigourous completion of QED, or string theory etc. The question is appropriateness. Would it be right for me to interrupt every thread about relativistic QED by saying that there is no proof that relativistic QED even exists? Here the start of the thread is just simple QM, and I used collapse in a completely standard shut up and calculate way, and there is the interruption that this is somehow not standard.

BTW, this is not the paper I was thinking of which dealt with collapse in the minimal interpretation, but here is one that deals with a physical collapse http://arxiv.org/abs/1111.1425.

 

[atyy]

There is a problem with your request and I don't know why atyy doesn't point it out!
Collapse is not supposed to be a time evolution in the same sense as the unitary evolution you're talking about. Its not supposed to be a fundamental evolution besides the unitary evolution. Its not even supposed to be in a fundamental theory!
The crucial point was clearly explained by @stevendaryl but looks like it was ignored. When considering an open quantum system, an effective evolution seems to emerge for the (open) system. We're still unable to completely derive this effective evolution from the fundamental unitary evolution of the larger closed system. That's why we just consider its input and output and treat it as a blackbox and call it by such a mysterious name as collapse. When this blackbox is explained, we all expect to retain the unitary evolution that is compatible with Poincare group. So even if there is an incompatibility with the Poincare group, its because we're considering an effective evolution and ignoring part of the system.
Now it seems to me that the only point of disagreement here, can be whether that effective evolution actually emerges or not.

I think atyy doesn't point this out, because he doesn't agree that collapse can emerge from a larger theory.

I don't discuss this because if all you have is unitary evolution, you will end up with unitary evolution of the universe with all the problems of interpretation including MWI etc.

My aim in this thread is to defend the minimal interpretation or shut up and calculate because it works. Vanhees71 claims to support shut up and calculate or the minimal interpretation, but if you notice, it is he that is always bringing up issues of interpretation by objecting to collapse.

 

[ShayanJ]

I don't discuss this because if all you have is unitary evolution, you will end up with unitary evolution of the universe with all the problems of interpretation including MWI etc.

What's wrong with a universe that evolves unitarily?

My aim in this thread is to defend the minimal interpretation or shut up and calculate because it works. Vanhees71 claims to support shut up and calculate or the minimal interpretation, but if you notice, it is he that is always bringing up issues of interpretation by objecting to collapse.

As I said, it seems to me the only thing that can be a matter of disagreement here is that whether collapse happens for an open quantum system or not(whether its emergent as I say, or fundamental as you say, we should first establish that it happens because vanhees71 doesn't think that it does!). Can you give a reference that it does? I mean, experimentally. Something like this!(I'm not saying its a good example, just an example!)

 

[atyy]

@rubi: I haven't read it carefully, but the article I was thinking about is State Vector Reduction in Relativistic Quantum Mechanics: An Introduction by Breuer and Petruccione in the book "Open systems and measurement in relativistic quantum theory: proceedings of the workshop held at the Istituto italiano per gli studi filosofici, Naples, April 3-4, 1998, edited by Breuer and Petruccione.

http://omnibus.uni-freiburg.de/~breuer/paper/proc98-1.pdf

 

[zonde]

There is of course no counterexample to a proven theorem. Using frequencies instead of probabilities doesn't change that. The existence of a local probabilistic model that predicts the QM probabilities proves beyond doubt that these probabilities are compatible with locality. What's wrong with your counterexample? Frequency proofs of Bell's theorem make the same assumptions, they are just less obvious, because nobody is used to the frequency formulation. The choice of subsequences in the frequency formulation of probability is dual to the choice of a conditional probabilities in the measure formulation.

This paper https://arxiv.org/abs/1412.6987 is not published in peer reviewed journal so as I understand you leave it up to me to point out the flaws in this local model. Fine.

Statement that QM probability space is embedded in larger classical probability space means that model exploits detection loophole. However model avoids detectable unpaired detection by making both entangled particles for particular combination of Alice's and Bob's measurement settings undetected. So it makes detection or non detection at one side depend on the setting on the other side. Author of the paper sort of explains this in section 9.3. I will quote the whole section:

"Our model of embedding of the quantum probabilities in the Kolmogorov model can be considered as an extension of the space of hidden variables to include parameters generating selections of experimental settings. Such a hidden variable depends on the parameters for the selections of angles at both labs. One can say that a hidden variable is nonlocal (although observed quantities are local). However, this nonlocal structure of a hidden variable reflects the nonlocal setup of the experiment, and nothing else."

The statement in bold clearly says that this model is exploiting superdeterminism loophole and that is not acceptable in scientific model.

 

[zonde]

There is of course no counterexample to a proven theorem. Using frequencies instead of probabilities doesn't change that. The existence of a local probabilistic model that predicts the QM probabilities proves beyond doubt that these probabilities are compatible with locality. What's wrong with your counterexample? Frequency proofs of Bell's theorem make the same assumptions, they are just less obvious, because nobody is used to the frequency formulation. The choice of subsequences in the frequency formulation of probability is dual to the choice of a conditional probabilities in the measure formulation.

Now about your objections to my counterexample. There is no need to use frequencies in my counterexample. This counterexample boils down to the statement that there is no set of possible detections sequences that satisfy QM predictions (exactly) and locality conditions. If you are unsure about provided argument you can take some limit for detection sequences and test all possible combinations using brute-force search but as I see, the argument why it is not possible is rather trivial and does not require such a test to see the point.

If you rely on authority more than checking the arguments yourself there is Eberhard's paper http://link.aps.org/doi/10.1103/PhysRevA.47.R747. In this paper Eberhard has included Bell type inequality proof that takes similar approach as in the counterexample I gave.

 

[ShayanJ]

This paper https://arxiv.org/abs/1412.6987 is not published in peer reviewed journal

http://www.worldscientific.com/doi/10.1142/S1230161216500086

 

[zonde]

http://www.worldscientific.com/doi/10.1142/S1230161216500086

Forum guidelines contains a link where one can check acceptable sources http://ip-science.thomsonreuters.com/mjl/
I can not find WorldScientific there.

 

[vanhees71]

The minimal interpretation is agnostic about "cause". "Local interactions" are properties of Hamiltonians. The collapse does not even affect the Hamiltonian, so how can the collapse be related to interactions?

Come on, if you say there is a collapse, it can only be caused by the interaction of the particle with the measurement apparatus. If you say there is no interaction, you cannot measure anything.

 

[DrClaude]

Forum guidelines contains a link where one can check acceptable sources http://ip-science.thomsonreuters.com/mjl/
I can not find WorldScientific there.

World Scientific is not a journal, but a publisher. The journal itself is Open Systems & Information Dynamics, and it's impact factor for 2015 is 1.3.

I think it is a proper peer-reviewed journal and that it falls within the guidelines at PF. That said, because something has been properly published doesn't mean that is mainstream science or even right. But discussion of that paper will be allowed here.

 

[rubi]

This paper https://arxiv.org/abs/1412.6987 is not published in peer reviewed journal so as I understand you leave it up to me to point out the flaws in this local model. Fine.

The model in the paper was published in a reputable journal in the reference [12] of that paper. The paper is just a cooked down version of that reference.

Statement that QM probability space is embedded in larger classical probability space means that model exploits detection loophole.

The model considers all detections, so it doesn't exploit the detection loophole. Moreover, the model uses a different method to embedd the probabilities into a Kolmogorov space. It doesn't use marginals, but rather conditionals.

The statement in bold clearly says that this model is exploiting superdeterminism loophole and that is not acceptable in scientific model.

The model doesn't exploit the superdeterminism loophole, because it is not deterministic. Only a deterministic theory can be superdeterministic. The model however is purely stochastic. The non-local variables occur in the conditional probabilities and that is natural, since the quantum probabilities depend on the angles of both Alice and Bob, so we must condition on a non-local pair of angles to obtain the quantum probabilities. The author shows that despite of this, one obtains a local stochastic model.

Now about your objections to my counterexample. There is no need to use frequencies in my counterexample. This counterexample boils down to the statement that there is no set of possible detections sequences that satisfy QM predictions (exactly) and locality conditions. If you are unsure about provided argument you can take some limit for detection sequences and test all possible combinations using brute-force search but as I see, the argument why it is not possible is rather trivial and does not require such a test to see the point.

If you rely on authority more than checking the arguments yourself there is Eberhard's paper http://link.aps.org/doi/10.1103/PhysRevA.47.R747. In this paper Eberhard has included Bell type inequality proof that takes similar approach as in the counterexample I gave.

As I said, the use of subsequences in frequency versions of the inequality amounts exactly to the use conditionals in the probability setting. You can't just select a subsequence and expect it to be distributed in the same way as the original sequence. This assumption must be made in all proofs of the inequality. The inequality can't be proved without this assumption.

@atyy: I haven't had time to read your papers yet, but I will respond later.

 

[vanhees71]

On my part, I don't know what to think. On one hand, the long-range correlations are there because of measurement, and avoiding collapse doesn't practically account for compound measurements (you have to believe it would work if you could do the practically impossible calculation of treating the whole measurement device quantum mechanically). On the other hand, collapse is frame-dependent, although the consequences are the same whatever frame you choose in the end, so it seems to beg for a deeper explanation.

This discussion is a mess, and I'm sorry that I got involved into it again. The physics is very clear, and there is no problem.

An experiment happens in the lab and not in Hilbert space. Let's take the example of the Aspect-like experiment. There, via parametric downconversion a polarization-entangled photon pair is produced by shining a laser into a certain type of birefringent crystal. The interaction of the em. field produced by the laser is local (according to QED). It is localized in the sense that it takes place in the crystal and thus the extension of the interaction region is at most the size of the crystal (a few $\mathrm{cm}^3$ I'd say). Via some optical devices you have a two-photon state with the polarization part given as
$$|\psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle - |VH \rangle).$$
According to the usual rules of probabilities to get the polarization state of the single photons you have to trace over the other photon, i.e., you have
$$\hat{\rho}_A=\mathrm{Tr}_B |\psi \rangle \langle \psi |=\frac{1}{2} \hat{1},$$
and the same for $\hat{\rho}_B$. As you see the single-photon polarizations are completely undetermined, i.e., you have unpolarized photons.

Now Alice (A) and Bob (B) perform a polarization measurement with the polarizer in H direction at very far distant places, such that according to the finite signal propagation (maximal speed is the speed of light) the measurement of A's photon's polarization cannot affect B's photon's polarization at the moment he is measuring it. Within QED this is ensured by the locality of the interaction of the photons with the measurement device and the microcausality of QED (it's built in into the theory by construction!).

Now, although both photons are precisely unpolarized due to the entanglement of the prepared photon pair the polarization measurements are strictly correlated. According to the rules of QT the probabilities for the four possible outcomes (VV, HH, VH, HV) are
$$P_{HH}=|\langle HH|\psi \rangle|^2=P_{VV}=|\langle VV|\psi \rangle|^2=0, \quad $$P_{VH}=P_{HV}=\frac{1}{2}.$$
So although the photons are completely unpolarized there's a correlation for the pairs. You never find both H polarized or both V polarized but always with perpendicular polarizations. If A measures H B measures V and vice versa.

According to this description this correlation is due to the preparation of the two-photon state in the very beginning and not due to the polarization measurement of A or B. Note that also A and B can find this correlation only by exchanging information according to their precise measurement protocols, i.e., both must keep track of the times they register the photons to know which two photons come from one pair and then afterwards they can check the correlation. In no way can you propagate instantaneously information by such a setup.

Also note that there's no collapse of the state as a whole via the measurement of either A or B. It's only such that if A finds H, she knows that B's photon will be found to have polarization B, but for Bob that doesn't change anything, i.e., the only thing he knows is that he will find with probability 50% either H or V. Also A finds with 50% probability H. So everything is consistent, and there is no spooky action at a distance, which is implied by the assumption of a collapse, but as you see, we don't need the collapse to understand the correlations. Further according to QT you cannot say more about the outcome of these measurements than the said probabilities, and the understanding is that the polarization of the single photons is really maximally indetermined.

In the hope that there may be a way to mimic these QT probabilities with a deterministic theory one came up with the idea of hidden variables which take determined values in any case and they are just unknown to A and B. Now Bell has shown that this assumption together with locality of interactions (between the photons and the polarization measurement devices) leads to an inequality for certain correlation functions, which is violated by QT (here QED which uses local interactions only by construction!). Indeed in corresponding experiments with such entangled photons (here you have to set the relative angle of the polarizers to another value than 0 or $\pi/2$) that the Bell inequality is violated with an astonishing significance (google for Zeilinger to find the details) and with the same significance the QT prediction is confirmed. The conclusion is that there is at least no deterministic hidden-variable theory with local interactions that is in accordance with QT and the observations. Only QT (in this case QED) admits the locality of interactions at the same time with the strong correlations described by entanglement which in the sense of violating Bell's inequality are stronger than the correlations possible for local hidden-variable theories.