I Are entanglement correlations truly random?

entropy1

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That definition doesn't work. A trivial counterexample would be the string S' that I get by flipping every bit in a random string S; S' is no less random than S itself (all I'm doing is changing the symbols that represent the string), yet there is a 100% anticorrelation between the two.
In my view that would have to be flipping bits randomly (flip/no-flip). By flipping every bit you are creating a (anti-)correlation. That would be similar to the correlation an entanglement would yield. The fact that there is a correlation is what sets this kind of 'randomness' apart from the example with two independent sources. If you compare two 'truly' random ('independent') strings, you won't get a correlation in any aligment. The strings from a source like an entanglement experiment that have a correlation only yield a correlation when the strings are aligned absolutely. In any other alignment they are random (p=0.5). It is the correlation that sets correlating bitstrings apart from, in my definition, 'true' random bitstrings.

Entanglement data and artificially generated correlations (like in my code) are identical with respect to my argument. It is just that correlating data is random in every other alignment. That would be random, were it not that in exactly one alignment they correlate. This differs from independent random sources. It is this difference that sets correlating data apart, in my view.

Correlation is, as it were, a 'hidden payload'.
 
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the problem is, what is randomness ?
 

entropy1

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the problem is, what is random ?
Random correlation (no correlation, p=0.5). (in any/every alignment of bitstrings)

As I define it, that is. :wink: However, if it is a question of definition, I can choose my own, right? :smile:
 
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entropy1

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Big problem, too. Any known test for it can be demonstrated to give false positives.
Maybe all harmonics equally present? If we can't define random, how come we use the term?
 
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Maybe all harmonics equally present? If we can't define random, how come we use the term?
Not sure what you mean by "harmonics." Good point, though. Random streams are used a lot in software for things like generating probable primes, calculating pi, etc. They're just not "truly" random in that they might manifest (be manifestations of) an underlying orderliness/predictability.
 

DrChinese

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...That would be similar to the correlation an entanglement would yield. The fact that there is a correlation is what sets this kind of 'randomness' apart from the example with two independent sources. If you compare two 'truly' random ('independent') strings, you won't get a correlation in any aligment. The strings from a source like an entanglement experiment that have a correlation only yield a correlation when the strings are aligned absolutely. In any other alignment they are random (p=0.5). It is the correlation that sets correlating bitstrings apart from, in my definition, 'true' random bitstrings.

Entanglement data and artificially generated correlations (like in my code) are identical with respect to my argument. It is just that correlating data is random in every other alignment. That would be random, were it not that in exactly one alignment they correlate. This differs from independent random sources. It is this difference that sets correlating data apart, in my view.

...
Admittedly, my comments are not a direct analog of what you are discussing. However, there are entangled pairs created from fully independent source lasers. Those photons have never been in causal contact or otherwise present in the same region of spacetime. They are correlated, of course, as they are entangled. Each appearing random as to polarization when examined separately.
 

entropy1

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Admittedly, my comments are not a direct analog of what you are discussing. However, there are entangled pairs created from fully independent source lasers. Those photons have never been in causal contact or otherwise present in the same region of spacetime. They are correlated, of course, as they are entangled. Each appearing random as to polarization when examined separately.
I would say those sources are not independent. If they are, there would have to be hidden variables, but that would yield different results. Otherwise I can't imagine such an experiment.
 
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Maybe all harmonics equally present? If we can't define random, how come we use the term?
God only knows.
BTW, I can't define God.
 
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However, there are entangled pairs created from fully independent source lasers. Those photons have never been in causal contact or otherwise present in the same region of spacetime. They are correlated, of course, as they are entangled. Each appearing random as to polarization when examined separately.
Your remark got me wondering, is there any evidence that entanglement actually involves any interaction between particles? As in, do they actually exert any sort of influence on each other, or are they just similarly seeded/configured? Analogous say to a "random" number generating algorithm, which will always, given the same seed, generate the same sequence of values, regardless of frame of reference. With the particles, the seed is physically configured, so maybe more akin to similarly loaded dice.
 

DrChinese

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I would say those sources are not independent. If they are, there would have to be hidden variables, but that would yield different results. Otherwise I can't imagine such an experiment.
Just to be specific:

https://arxiv.org/abs/0809.3991
"High-fidelity entanglement swapping with fully independent sources"
Rainer Kaltenbaek, Robert Prevedel, Markus Aspelmeyer, Anton Zeilinger

The swapping operation entangles a pair of photons that were produced from fully independent sources. Of course the pairs are post-selected, but their polarization will be as random as it gets. And correlated with each other.
 

DrChinese

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Your remark got me wondering, is there any evidence that entanglement actually involves any interaction between particles? As in, do they actually exert any sort of influence on each other, or are they just similarly seeded/configured? Analogous say to a "random" number generating algorithm, which will always, given the same seed, generate the same sequence of values, regardless of frame of reference. With the particles, the seed is physically configured, so maybe more akin to similarly loaded dice.
Well in some respects, I would agree: entangled particles are similarly "seeded". But I would exercise restraint with that statement too. Bell tells us that they can't contain local hidden variables that predetermine outcomes. For example, a pair entangled as to spin is in a superposition until measured.
 

Simon Phoenix

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It is just that correlating data is random in every other alignment. That would be random, were it not that in exactly one alignment they correlate. This differs from independent random sources. It is this difference that sets correlating data apart, in my view.
You seem to me to be making very heavy weather of the notion of statistical dependence in these posts - but then again, as I've said, maybe I'm missing the point of what you're saying.

I'm not sure what your notion of 'alignment' is trying to say - it's kind of obvious/trivially true and I can't yet see the utility of it. Take a uniformly random binary string*. Clearly there's no correlation between bit ##j## and bit ##k## (otherwise it wouldn't be a uniformly random string). But that's all you're saying with the notion of alignment you've described.

I can't really see that you're saying anything different in your posts than if we have dependent distributions for two events ##A## and ##B## then the joint distribution ##p(A,B)## is not equal to the product of the marginal distributions ##p(A)p(B)##

But I may very well have misunderstood what you're trying to say.

In information terms we would say that two distributions are correlated (dependent) if knowledge of one of the events reduces our uncertainty about the other event. Coming back to Chris' allusion to crypto we can see this is a useful parameter. If we have access to a ciphertext (eavesdropping) does this reduce our uncertainty about the message that was sent? If it does then there is some information about the message we can recover from the ciphertext. So assuming a secret key (that is, maximal uncertainty about the key) the only way to have zero information about the message in the ciphertext is to use a one-time pad. So in all crypto (except one time pads) there ##is## information in the ciphertext - the idea is to make this information unrecoverable to a polynomial time adversary.

*"string" here is again used as a shorthand because we're really properly talking about distributions.
 

entropy1

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Do you mean entanglement swapping?

You seem to me to be making very heavy weather of the notion of statistical dependence in these posts - but then again, as I've said, maybe I'm missing the point of what you're saying.
My proposal is, I think, really straightforward to get. I'll see if I can work my code into a graphic illustration. Maybe that illuminates the idea a bit. :smile:
 

DrChinese

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Do you mean entanglement swapping?
Yes, per the title of the paper. :smile:

The resulting entangled photons (after the swap) are from fully independent sources and have never interacted or even existed in a common light cone. The sources are phase locked together via a synchronizing signal. Note that the swap can occur after the entangled pair is observed, and in fact the entangled photons need not have ever existed at the same time.
 

entropy1

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Yes, per the title of the paper. :smile:

The resulting entangled photons (after the swap) are from fully independent sources and have never interacted or even existed in a common light cone. The sources are phase locked together via a synchronizing signal. Note that the swap can occur after the entangled pair is observed, and in fact the entangled photons need not have ever existed at the same time.
You could also see that as two dependent pairs of entangled particles (or measurements), that get dependent of each other by the swap. But then you have to suppose that an entangled pair is inherently dependent, which not seems that unreasonable to me. :rolleyes:
 

DrChinese

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You could also see that as two dependent pairs of entangled particles (or measurements), that get dependent of each other by the swap.
That how I see it. Of course, the swap occurs in a separate volume of spacetime from either of the final entangled pair. And can occur in any causal sequence relative to the creation or measurement of the final entangled pair.

In my view, the resulting outcome pairs are truly random even if redundant.
 

entropy1

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That how I see it. Of course, the swap occurs in a separate volume of spacetime from either of the final entangled pair. And can occur in any causal sequence relative to the creation or measurement of the final entangled pair.

In my view, the resulting outcome pairs are truly random even if redundant.
But the final measurements (particles 1 and 4) would be dependent, right?
 

DrChinese

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But the final measurements (particles 1 and 4) would be dependent, right?
Particles 1 & 4 (the final entangled pair) are fully independent in the sense that they were never in the same region of spacetime, nor did they ever interact with a particle that had previously interacted with the other in any manner.

The dependent part would only be that there is a correlation.
 
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The dependent part would only be that there is a correlation.
Correlated, strangely similar maybe, but given that they don't even have to exist at the same time, it's hard to conceive of a connection... unless through some higher dimension?
 

Simon Phoenix

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My proposal is, I think, really straightforward to get.
Yes - basically think of putting your binary string on a wheel. Now copy it and put this on an 'inner' wheel. Rotate the inner wheel. With overwhelming probability there's only one position of the two wheels where there is perfect correlation between the bits in the same positions on the wheels.

Now do the same but with 2 independently produced random strings - now, with overwhelming probability, there will be no position we can rotate to for which there's a perfect correlation.

But so what? I really don't see where you're going with this, or how it is helpful. There may well be something useful in this perspective - it's just I'm not seeing it yet.

All you're talking about here is the notion of statistical dependence - kind of statistics and probability 101. You're just talking about the difference between independent and dependent events. So far there's precious little in any of this to do with entanglement. The fact that things can be perfectly correlated is not the defining feature of entanglement (look up Bertlmann's socks)

Another model that's useful - think of a binary symmetric communication channel. We have Alice's input and Bob's output.

Alice inputs the symbol 1 with probability 1/2 and the symbol 0 with probability 1/2.

For the symmetric channel Bob will record the symbol 1 with probability 1/2 and the symbol 0 with probability 1/2.

Now if there's no noise on the channel if Alice inputs 1, Bob receives a 1. Same for the symbol 0. In this case there's perfect correlation and the message is received without error (the coins joined by a rigid rod example). If there's perfect noise on the channel there's no correlation now between Alice's input and Bob's output and so no information can flow (two independent coins being tossed).

If it's a binary symmetric channel the marginal probabilities remain the same - but the conditional probabilities change as we change the noise characteristic of the channel.

What are you saying in your posts that's any different to this example of dependence vs independence?
 

Simon Phoenix

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it's hard to conceive of a connection... unless through some higher dimension?
DrChinese has given the example of full entanglement swapping, but there's a kind of 'half-way house' that might help to shed some light.

Imagine a perfect optical cavity (the experiments were done in very high-Q microwave cavities). Now take a 2 level atom in its excited state (Rydberg atoms can be used as a reasonable approximation to a 2 level atom). Fire this atom through the cavity with a specific transit time such that the field and atom become perfectly entangled.

Now suppose we live in an ideal world and we can maintain the entanglement between the cavity field and the atom. Go make a cup of tea. Ship the atom off to the outer moons of Saturn.

Now take a second atom prepared in its ground state and fire this through the cavity with a different tailored transit time through the cavity. Tailor this time just right and after this second atom has gone through the cavity the 2 atoms are now entangled and the cavity field 'decoupled'.

The two atoms have never directly interacted - and (if we can maintain the entanglement long enough) the two atoms can be fired through the cavity years apart.

OK that's wildly fanciful in terms of shipping things off to Saturn and maintaining entanglement for years - but the experiments have been performed (although with more modest parameters).
 

entropy1

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Yes - basically think of putting your binary string on a wheel. Now copy it and put this on an 'inner' wheel. Rotate the inner wheel. With overwhelming probability there's only one position of the two wheels where there is perfect correlation between the bits in the same positions on the wheels.

Now do the same but with 2 independently produced random strings - now, with overwhelming probability, there will be no position we can rotate to for which there's a perfect correlation.
Told you it was simple. :biggrin: Unfortunately I think I have to refrain from replying to your post because I fear I would go far off topic. But I'll give your post a good contemplation. :smile:
 
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This is all very confusing... just thinking out loud...

I flip a coin and it lands heads. Does it still make sense to describe the probability of a heads for that flip as p=.5, ten minutes after the fact? Does probability even exist for events in the past? If the flip occurred within a closed box, opened after ten minutes, it seems my probability before opening the box, of guessing heads correctly, is p=.5, but the coin's probability of heads went to p=1 at the end of the unseen flip... and my probability of guessing heads correctly goes to p=1 as soon as the box is opened... but I don't think that is how it is done.

I have a sequence to which a subsequent element is appended every ten minutes (maybe a coin flip). While waiting for the next element I produce a rule that specifies all the elements so far, and when each next element arrives I adjust the rule to succeed incorporating the inclusion of that one. Is a finite string characterized by a rule random? I don't think that is how it's done either.

Both of these thoughts goes to a time relationship of randomness... does the standard treatment not take time into account? It looks to me like things that have not happened yet (hypothetical) may be characterized as probabilistic or random, but once these things happen and are made manifest*, they may be characterized as having a probability of 1, or characterized by a complete generating rule.

* Have probability and randomness joined with length, time, and simultaneity respecting relativistic measures?
 

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