Quantum entanglement information

[calinvass]

It is said that the measurement done on a particle instantly affects its entangled pair because Bell's theorem excludes a hidden variable. That means there is a cause and an instant effect at a distance. Say we have two entangled particles A and B. If there is no hidden variable then the state of the particles are not definite until measured. After we measure the first particle and find it with spin |up> for example, does it mean now particle B is in a definite state |down>?
If we consider both particles as a single system, after the measurement of the first particle is the system state determined on the measurement axis?

 

[DrChinese]

It is said that the measurement done on a particle instantly affects its entangled pair because Bell's theorem excludes a hidden variable. That means there is a cause and an instant effect at a distance. Say we have two entangled particles A and B. If there is no hidden variable then the state of the particles are not definite until measured. After we measure the first particle and find it with spin |up> for example, does it mean now particle B is in a definite state |down>?
If we consider both particles as a single system, after the measurement of the first particle is the system state determined on the measurement axis?

Yes, it acts as single system. It is "as if" there is a distant "effect". As far as anyone can tell, the nature of a measurement "here" leads to a matching change "there".

I don't know I would characterize it as a "cause" though, as the specific result is random. Also, there is no causal direction to speak of, as the sequence of measurements seems to make no difference.

 

[PeterDonis]

That means there is a cause and an instant effect at a distance.

No, it doesn't. It just means that quantum entanglement cannot be modeled using local hidden variables.

The proper definition of "causality" is that spacelike separated measurements must commute, i.e., the results can't depend on the order in which the measurements are made. Spacelike separated measurements made on entangled particles satisfy this requirement. Note that this requirement says nothing about "instant effect at at distance"; there is no need to invoke that. Such a need would only be present if the results of the measurements depended on which one was done first.

 

[calinvass]

If the events are spacelike separated they cannot be cause and effect and since they states are ways opposite there should have a common cause which points to a hidden variable. If there is no hidden variable then there is an instant effect at a distance. It is clear that there is no effect at a distance. It is also clear that there is no hidden variable. It is also clear that the above conclusions are contradictory.
No communication theorem doesn't demonstrate information doesn't travel faster than light but only we cannot send information (either faster than light or not )using entanglement.

 

[DrChinese]

1. ...since they states are [al]ways opposite there should have a common cause which points to a hidden variable. ...

2. If there is no hidden variable then there is an instant effect at a distance.

A reasonable assumption (perfect correlations imply HV), but one which is consistent only with instantaneous action at a distance.

Your statement 2. is incorrect (you have it backwards). If there ARE Hidden Variables, then there must be instantaneous action at a distance.

 

[bhobba]

No, it doesn't

Put a green slip in an envelope and a red slip in another - open one and you instantly know the other. No communication, spooky action at a distance and any of the other stuff touted about entangled systems. Entangled systems, like the pieces of paper are simply correlated.

Here is the real issue. Quantum correlation has some statistical properties different to classical correlation. The reason is we know at all times in the paper slip example that the paper is red or green. In QM we do not know what properties it has unless actually observed. This leads to the different statistics - but again - its just a correlation - no more, no less.

Now what does Bell say. Well first Bell was a genius in the same class as Einstein, Feynman, Von-Neumann etc - he saw to the heart of the matter when others did not. And that heart is simple - want it to be like the slips of paper - then there must be non local influences going on. But just accept QM as is then no problem. That's it, that's all. Nothing too complicated really - but of course it took the genius of Bell to see it.

He even wrote a paper explaining it that way except he used the amusing Bertlmann's socks analogy, rather than slips of paper:
https://cds.cern.ch/record/142461/files/198009299.pdf

BTW please don't post about the math - he leaves out some steps - they are not hard to do but are tedious and you can pretty much see they are true without even doing the math.

Thanks
Bill

 

[m k]

In QM we do not know what properties it has unless actually observed.

Can't we see a statistical difference between polarizations if other half of stream of polarization entangled pair is put thrue a slit?

 

[bhobba]

Can't we see a statistical difference between polarizations if other half of stream of polarization entangled pair is put thrue a slit?

Yes - but the slit is an observation.

Thanks
Bill

 

[calinvass]

Your statement 2. is incorrect (you have it backwards). If there ARE Hidden Variables, then there must be instantaneous action at a distance.

"Einstein, Podolsky, and Rosen argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement without action at a distance. Later, Bell's theorem suggested that local hidden variables of certain types are impossible, or that they evolve non-locally."Wikipedia.
I suppose you meant non local variables.

 

[Nugatory]

"Einstein, Podolsky, and Rosen argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement without action at a distance. Later, Bell's theorem suggested that local hidden variables of certain types are impossible, or that they evolve non-locally."Wikipedia.

There is a reason why wikipedia is not, in general, an accepted source here... Often it's good, sometimes it's not so good, and sometimes it's just confusing. If you believe that it's in conflict with what @DrChinese posted, then we have an example of it being either wrong or confusing.

If you want to know whether a particular theory is precluded by Bell's theorem, you can consider whether it conforms to all the assumptions that Bell made when he derived his inequality. If it does, then it must obey the inequality and therefore we reject it as not consistent with experimental results. If it does not, then as far as Bell's theorem is concerned it may or may not be a valid theory and we have to look elsewhere for reasons to accept or reject it. You can drag words like "reality", "locality", "hidden variables" into the discussion, but unless you clearly connect these words to the assumptions that go into the derivation of the inequality you're unlikely to find any new insight and likely to find yourself in a sterile argument about which words to apply to any given theory.

 

[calinvass]

I'm sorry.
I only wanted to clarify this. Does "No communication theorem" alone demonstrate information cannot travel faster than light?

 

[Nugatory]

I'm sorry.
I only wanted to clarify this. Does "No communication theorem" alone demonstrate information cannot travel faster than light?

No. It does prove that measurements on an entangled system do not transmit information at any speed, whether faster than light or not.

It says nothing about other possible ways of transmitting information, but of course relativity has a lot to say on that question.

 

[calinvass]

Thank you. I still don't understand why this conclusion. I can only deduce that we cannot send information using entanglement (there is nothing we can do on a entangled particle to be detectable by measuring its entangled pair), not even at lower speed than c. I'm not arguing that information can travel faster than light.

 

[slufoot]

does the effect of observation have an effect upon the observed partial ?

 

[Mathematech]

Bell was hardly a genius, his inequalities were a known result in Statistics going back to the work of George Boole and are not specific to hidden variable theories. He also had an agenda. The understanding of statisticians is that if data violates these inequalities then the observables have been chosen inconsistently - something which we in fact know upfront because we are trying to treat incompatible observables as compatible. But Bell tries to imply that there is spooky action at a distance occurring.

 

[vanhees71]

Obviously you haven't understood the crucial point of Bell's great work on the foundations of QT. It's not less than making a purely metaphysical question about the inseparability of parts of entangled quantum systems, the feature of QT which quibbled Einstein, Schrödinger, and others the most about QT, a scientifically testable prediction. Particularly at the time of Boole, nobody knew about a probabilistic model like QT.

The probabilities in QT, or more specifically the strong correlations, which can be of arbtrarily long range, described by entanglement, are objectively different from any correlations that are possible in local deterministic theories. So quantum theory is distinct from any local deterministic hidden-variable theory and thus both types of descriptions of nature can be objectively tested in experiment. In the recent years the evidence has become overwhelming that QT is the correct description of Nature rather than local hidden-variable theories. This is a great foundational breakthrough, resolving the objections raised by EPR in the 1930ies, in favor of QT.

Within the minimal statistical interpretation of QT, which in my opinion is the only consistent purely scientific interpretation yet, no instantaneous information exchange is possible through entanglement. It describes only the strong and often long-distance correlations of subsystems of systems prepared in a state, for which certain observables are entangled, e.g., the polarization of photon pairs created by parametric down-conversion. These photons can be detectected arbitrarily far away and still showing the corresponding correlations. Each observer of the single photons, however, sees only perfectly unpolarized photons (maybe it's the most accurate way to provide ensembles of really unpolarized photons possible). Only if both observers take accurate measurement protocols, including precise time stamps of the photon detection, that enable to be sure about the pairs of photons that belong to one entangled state, you can find the 100% correlations between the polarization states of the polarization-entangled photons, and thus you cannot instantaneously transfer information over far distances. To the contrary, any attempt to manipulate one of the photons leads to disentanglement, i.e., you have to measure the single photons' polarization without manipulating each of them before to see the correlations described by entanglement.

 

[Mathematech]

Actually you have failed to understand just how much people like Boole and Kolmogorov did understand about sets of observables being incompatible and how this occurs even outside physics.

 

[morrobay]

The probabilities in QT, or more specifically the strong correlations, which can be of arbtrarily long range, described by entanglement, are objectively different from any correlations that are possible in local deterministic theories. So quantum theory is distinct from any local deterministic hidden-variable theory and thus both types of descriptions of nature can be objectively tested in experiment.
.

Within the minimal statistical interpretation of QT, which in my opinion is the only consistent purely scientific interpretation yet, no instantaneous information exchange is possible through entanglement. It describes only the strong and often long-distance correlations of subsystems of systems prepared in a state, for which certain observables are entangled, e.g., the polarization of photon pairs created by parametric down-conversion. These photons can be detectected arbitrarily far away and still showing the corresponding correlations. .

Paragraph 1 above : With spin 1/2 particles and the perfect anti correlations at SG parallel detector settings that the inequality is derived from. I understand why the hidden variable notion is ruled out when inequality does not hold for miss-aligned settings, based on the sin² and cos² formulas.

Paragraph 2 above: With this description that accounts for the spacelike separated photons' non classical correlations: I am confused on how this is different from a hidden variable description ? I read this as the correlations were created during entanglement
preparation ( common past cause). And this information that determines the photons response to a polarizer angle are carried with the photons from production to detection. A (α,λ) = ± 1. B( β,λ) = ± 1.

 

[vanhees71]

Exactly. So where is your problem?

 

[morrobay]

Exactly. So where is your problem?

Then are you saying that the minimal statistical interpretation is a hidden variable local theory that agrees with QM predictions ? Thats fine with me.However my understanding is that the inequality violations rule out LHV,s

 

[vanhees71]

No, the minimal statistical interpretation is, as the name says, just QT without any metaphysical additions, which are given the empirical facts unnecessary. The complete description of the polarization state of the two-photon system is given by (I take the most simple example)
$$|\Psi \rangle=\frac{1}{\sqrt{2}}( |HV \rangle-|VH \rangle$$,
i.e., the two-photon system is prepared in the pure state
$$\hat{\rho}=|\Psi \rangle \langle \Psi |.$$
All you know, and all you can know about arbitrary polarization measurements on the two photons, is the probabilistic information encoded in this state according to Born's rule.

An observer who measures only one photon, will describe it by the reduced statistical operator,
$$\hat{\rho}_A=\mathrm{Tr}_B \hat{\rho}=\frac{1}{2} \hat{1}.$$
So he/she will observe prefectly unpolarized photons.

On the other hand, if A and B both check whether their photons are horizontally or vertically polarized, they find a 100% correlation, as encoded in the state ##\hat{\rho}##, i.e., with probability ##1/2## A finds H and B V and with probability ##1/2## A finds V and B H. HH and VV never occur. An that's all you can say about the so prepared two-photon system. There's no hidden information anywhere.

In other words, according to the minimal interpretation, there is nothing else possible to know about photons than what can described within QED, and thus no hidden-variable theories are needed. The strong correlations are described by entanglement as in the above example, no more no less.

As long as there is no empirical evidence against what's predicted by QED, any thinking about (necessarily non-local) deterministic hidden-variable theories is a waste of time!

 

[zonde]

The proper definition of "causality" is that spacelike separated measurements must commute, i.e., the results can't depend on the order in which the measurements are made. Spacelike separated measurements made on entangled particles satisfy this requirement.

We can only say that statistical properties of spacelike separated measurements made on entangled particles commute. You can't say that about individual detections. Because commutativity of individual measurements does not follow from commutativity of statistical properties of many individual measurements. To see this you can consider a toy model.
We have a series of boxes where each box contains two identical balls except that one ball is red but the other one is blue.
Alice without looking takes one ball from each box. Bob gets the other one. Clearly which ball Alice takes from the box affects which ball will be left for the Bob. So Alice's action affects Bob's result. But statistical properties for Alice's and Bob's "measurements" do not depend in what order they draw the ball.

 

[DrChinese]

Bell was hardly a genius, his inequalities were a known result in Statistics going back to the work of George Boole and are not specific to hidden variable theories. He also had an agenda. The understanding of statisticians is that if data violates these inequalities then the observables have been chosen inconsistently - something which we in fact know upfront because we are trying to treat incompatible observables as compatible. But Bell tries to imply that there is spooky action at a distance occurring.

Boole died long before quantum mechanics appeared, so clearly no application to physics on that score. And you allege Bell had an agenda past advancing physics? Seriously? And yes, Bell's Theorem can be said to imply spooky action at a distance - but that is strictly interpretation dependent. as is quite clear from him paper.

So yours is one of the strangest commentaries I have seen on Bell. And far from general consensus. If you are going to make some outlandish statements such as this, it would be appropriate to back it up with suitable references.

 

[Mathematech]

Take a look at this paper for example https://www.researchgate.net/publication/51931411_Hidden_assumptions_in_the_derivation_of_the_Theorem_of_Bell

The authors think that Bell probably didn't know of Boole's result but reading Bell, such as his discussion of Bertlmann's socks and comparisons with surveys of sock washing, it is clear that he was well aware of the techniques in use by statisticians even if he did not know that it was Boole who had come up with it. And yes Boole was well before QM, Boole was simply dealing with things like surveys and whatever it is that actuaries do. But that's the point, even in these fields you get things happening that cannot be explained as different ways of cutting the same cake. Kolmogorov was also aware of this and of the inadequacies of his formalization of probability in terms of measure spaces.

That QM gives different statistics to a standard Kolmogorov probability space was well known to von Neumann for example, well before Bell. Bell does get credit for being the first to reiterate using inequalities typically used by statisticians.

 

[vanhees71]

Boole died long before quantum mechanics appeared, so clearly no application to physics on that score. And you allege Bell had an agenda past advancing physics? Seriously? And yes, Bell's Theorem can be said to imply spooky action at a distance - but that is strictly interpretation dependent. as is quite clear from him paper.

So yours is one of the strangest commentaries I have seen on Bell. And far from general consensus. If you are going to make some outlandish statements such as this, it would be appropriate to back it up with suitable references.

Yes, indeed. Ironically Bell's work on the foundations of QT made philosophical gibberish hard science, and this enabled experimental for some decades to bring the implications of entanglement (what Einstein called "inseparability", and which was his strongest obejction against QT) to the test, which confirmed QT with astonishing accuracy.

It's on the other hand clear that Bell's theorem does not imply spooky action at a distance, and it's tested mostly with photons, i.e., entities that are utmost relativistic, and they are described by local microcausal QED. So it's very clear by construction that the findings about the violation of Bell's inequality are compatible with local relativistic QFT and thus describe long-ranged correlations but no actions at a distance, as long as you don't insist on some "collapse mechanism", which in my opinion belongs to the philosophical gibberish rather than hard science anyway.

 

[Mathematech]

It's on the other hand clear that Bell's theorem does not imply spooky action at a distance

My point is, from what one reads every day in popular science articles and what one sees being asked on forums, it is not at all clear to the majority that Bell's theorem does not imply spooky action at a distance, quite the contrary, and this confusion was started by Bell.

There are several aspects (no pun intended) of Bell's theorem that the majority fail to understand. Firstly, that a "hidden variable theory" is not merely the supposition that the measurements are determined by hidden unknown properties of the particles, it also includes a requirement that the experimental averages and correlations be recoverable from the set of hidden variable values by means of standard Kolmogorov probability. Unfortunately many physicists think you can just integrate or average over any sort of mathematical structure - you can't. Even in simplified versions of Bell's theorem where counting arguments are used, there is an erroneous assumption that averaging counts over any sort of structure will result in the same averages and correlations obtained in experiment - it doesn't. (For example, arrange the natural numbers as follows 1,3,2,5,7,4,9,11,6,13,15,8... whoa! picking an odd number from the set of natural numbers is "obviously" twice as likely as picking an even ... except it isn't.)

Another point is that Bell's theorem supposes the confusingly named counterfactual definiteness, which does not simply mean that an experiment not performed can be assigned a definite outcome, but that such outcomes can be treated equally with actual experimental outcomes when averaging or calculating correlations, something which relates back to the point about the ability to recover experimental averages from hidden parameters - it doesn't work with counterfactual values of incompatible observables.

 

[vanhees71]

(For example, arrange the natural numbers as follows 1,3,2,5,7,4,9,11,6,13,15,8... whoa! picking an odd number from the set of natural numbers is "obviously" twice as likely as picking an even ... except it isn't.)

Can you explain to a simple theoretical physicist as me how you come to this strange conclusion by just reordering the natural numbers? I can also reorder them such as to least all odd numbers before all even numbers. Is then drawing an odd number impossible and if so why?

Of course, probabilities depend on the situation for which they are calculated, and whether you measure the calculated probabilities in random experiments on equally prepared ensembles is of course a question whether your experimental setup is correct or not, which itself has to be verified by carefull observations either, but what has this to do with Bell's work?

 

[Mathematech]

My conclusion is that it is NOT true that it is twice as likely to pick an odd number than an even ... is this what you are asking me to explain?

 

[vanhees71]

My point is that you clearly have to describe, how you draw numbers to make a hypothesis about the probabilities to draw an even or odd number and what it may have to do with their ordering. It is clear that associations of probabilities to concretely given situations are not governed by the axiomatic setup of probability theory (like the standard Kolmogorov axioms) but you need other input to do so.

QT is the physicists' way to evaluate probabilities for the outcome of experiments from given preparation procedures (aka quantum states). It's obviously not part of Kolomogov's axioms.

 

[Mathematech]

The point I was getting at with the natural numbers, take the arrangement I gave and calculate the average ratio of even to odd numbers for a large number of terms. It gives 1:2. Take the standard arrangement and you get 1:1. So what's the probability of getting an even number when randomly selecting a natural number?

 

[vanhees71]

I still don't understand, how you come to different ratios. The relative number of even and odd numbers are the same and it's the same as the number of natural numbers, because there's a one-to-one mapping between all these sets, and how you order the numbers doesn't make any difference, but I think it's anyway not to the point concerning Bell's work on the foundations of QT.

 

[Mathematech]

For the arrangement I gave, for each n, form the ratio of evens to odds in the first n terms of the arrangement.

 

[calinvass]

It is the same as having a dice with 3 faces, two green, one red, the probability of getting green is 2/3.

 

[Simon Phoenix]

it is not at all clear to the majority that Bell's theorem does not imply spooky action at a distance, quite the contrary, and this confusion was started by Bell.

I'm intrigued by your comments. For me, Bell has always been impeccably clear. In fact in these days of mostly terse, impenetrable, technical papers, reading one of Bell's works is rather refreshing

I don't see how Bell can be at all blamed for any confusion - quite the opposite - it is my view that with a stroke he cut through the befuddlement of earlier thinking on this subject. It is my view that he clarified things enormously by showing that some rather reasonable (classical) assumptions about correlated variables leads to those correlations being constrained. I think he pinned things down beautifully and precisely but I guess others might not see it like that.

Furthermore, as Vanhees has stressed he elevated a concept that was previously the realm of metaphysical mumblings and obfuscation into something that could be tested in the lab. Bell's work, by any reasonable standard, was a tour de force. It allowed a profound question about the nature of reality to be answered experimentally. Bell's theorem is crystal clear - it states in words that a local, hidden variable theory cannot reproduce all of the results of QM - and in such a way that we can test it. Maybe it's just me - but that's an absolutely stunning result.

How anyone can construe that this implies 'spooky action at a distance' is also quite beyond me, but there's no accounting for what goes on in other folks' heads

Another way of stating Bell's result would be to say that IF there are classical-like variables underlying nature, and discounting super-determinism, THEN these must have non-local dependencies (spooky action at a distance) in order to reproduce all of the results of QM - which is where I would guess the confusion comes from. But it's not right to blame Bell for this confusion - especially not when he wrote with such depth and clarity. He can't be blamed, I feel, for the subsequent confusion of others who misunderstood him.

In my view Bell's work on entanglement is one of the most profound and wonderful pieces of theoretical physics of the 20th century. Sure, according to my understanding, Boole showed, about a century before Bell, that for binary random variables ##A,B## and ##C## the joint marginals ##P(A,B), P(A,C)## and ##P(B,C)## could only be constructed from ##P(A,B,C)## in the usual fashion provided the pairwise joint distributions satisfied something we call the 'Bell inequality'. But how does Bell's rediscovery of this prior result lessen his achievement in any way? Even if Bell had been aware of Boole's earlier work I would still judge that his application of it was a tour de force as far as physics is concerned - but then as Hilbert once remarked "physics is much too difficult to be left to the physicists"

 

[Mathematech]

Bell quite explicitly pushed the idea that non-locality is required to explain violation of his inequalities, while at the same time being unaware that there could be anything wrong with his hand wavy integration over lambda. I have been reading his papers and to me its mind blowing how non-rigorous and flawed his arguments are regarding probability.