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crowded quantum information


hoola
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it does seem that there is a faster than light signalling with quantum entanglement issues, but that it cannot transfer any signal other than the basics used to determine a static outcome. Is this because no information can be "added on" to the basic mathematics that determines what is only allowed to happen in normal nature? Could it be possible to artificially "add on" signalling by building unique entangled structures that have a greater bandwidth?

Edited by hoola
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No, there is nothing superluminal going on between both parts of the bipartite state in Bell's theorem.

All the correlations are initial. Quantum correlations were there when the state was prepared.

They're there a Planck's time later.

They're there a millisecond later.

And they're there two hours later as long as you don't measure spin and let the state evolve coherently.

The moment you measure a spin component of one of the particles, correlations appear that cannot be explained in terms of the logic of three independent propositions in classical logic.

Physicist Alice measures something. If physicist Bob knows what she is going to do (assuming he trusts her), he can tell some things about the state he wouldn't be able to tell if Alice didn't measure.

Nothing is superluminal. Everything happens in the very weird internal space of elementary particles that we like to call the Hilbert space.

If you don't believe me, perhaps Murray Gell-Mann will convince you:

 

Edited by joigus
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 This does seem rather deterministic, and I thought that was not current thinking, but the gell man video wouldn't load, so will try later on that. It does seem as if the pairs sense no distance between them, and therefore act as such.

Edited by hoola
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32 minutes ago, hoola said:

 This does seem rather deterministic, and I thought that was not current thinking, but the gell man video wouldn't load, so will try later on that. It does seem as if the pairs sense no distance between them, and therefore act as such.

No, it's not deterministic. Quantum mechanics is fundamentally non-deterministic, and sure enough Gell-Mann adheres to it. He does argue at the end though in terms of his favourite interpretation of quantum mechanics, which is that of decoherent histories.

See how non-deterministic it is:

Alice: "I'm gonna go there and measure the x-component of spin"

Bob: "OK"

Now each one goes far away from each other and they conduct the experiment.

Alice measures the x-component of spin. Before she measures, she has no idea what it's gonna come out. See? Non-deterministic.

It happens to come out as "up". OK. Now she knows.

At the same time --in a reference system in which both are at rest-- Bob measures the x-component of spin. It sure turns out "down". Alice can tell him nothing, but now he can predict that Alice must have obtained "up" in her experiment, even though they're miles away from each other. He, of course, couldn't tell beforehand what he was gonna get. See? Non-deterministic on Bob's end too.

Both results are totally random separately (in fact they have maximal dispersion). Yet the Sx1+Sx2 is always zero. They're perfectly anti-correlated.

Each spin is random, but the sum is non-random (zero dispersion). See how it works?

Did that help?

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51 minutes ago, joigus said:

At the same time --in a reference system in which both are at rest-- Bob measures the x-component of spin. It sure turns out "down". Alice can tell him nothing, but now he can predict that Alice must have obtained "up" in her experiment, even though they're miles away from each other. He, of course, couldn't tell beforehand what he was gonna get. See? Non-deterministic on Bob's end too.

And, as far as I know, if Bob would postpone his measurement and still try to figure out the result he can only do so by getting the information from Alice. And signals between them are limited by the speed of light, so no faster than light exchange is possible.

+1 @joigus

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3 minutes ago, Ghideon said:

And, as far as I know, if Bob would postpone his measurement and still try to figure out the result he can only do so by getting the information from Alice.

Very fine point, but I think you're right. He may be able to devise a clever interference experiment though, to determine that someone's been messing with the state, because coherence has been broken. So he could determine in principle that Alice has performed a measurement, but he wouldn't be able to tell which outcome Alice got until he made the measurement.

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I have heard that is "how it works", but that doesn't explain the internal workings of the black box attributed to the idea. I did get the gell mann video to load, and having seen it several times before,  still leaves one with the impression that "it works this way because it works this way" and not a real explanation, nor much of a hint as to what is in the black box. I can  see one option and that is that quantum entanglements are independent from geometric space notions of distance and act as such being composed of i based mathematical numerical structures, and as so, rely on that structured, yet illogical underpinnings to explain their behavior.

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2 minutes ago, joigus said:

So he could determine in principle that Alice has performed a measurement, but he wouldn't be able to tell which outcome Alice got until he made the measurement.

Good addition, that seems true.


(Side note: If you were incorrect I think it would cause problems in quantum encryption and I've never seen such problems mentioned. but I would need to do some reading to confirm that)

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32 minutes ago, hoola said:

I have heard that is "how it works", but that doesn't explain the internal workings of the black box attributed to the idea. I did get the gell mann video to load, and having seen it several times before,  still leaves one with the impression that "it works this way because it works this way" and not a real explanation, nor much of a hint as to what is in the black box. I can  see one option and that is that quantum entanglements are independent from geometric space notions of distance and act as such being composed of i based mathematical numerical structures, and as so, rely on that structured, yet illogical underpinnings to explain their behavior.

The black box is in the mathematics of quantum mechanics. A particle can give you binary (up or down) projections of spin along any direction in a continuum of possible directions. So you would think, aha! the spin must be lying along some of these directions pointing in a certain way (up or down). If you assume this kind of classical logic, as Gell-Mann says, you're gonna have to conclude that there are negative probabilities, or instantaneous communication (non-locality), or both.

None of that happens. What happens is quantum mechanics.

Bell's theorem is a proof that whenever you have 3 propositions that are either true or not true (classical logic), eg:

A, not A

B, not B

C, not C

then the probabilities satisfy the following constraint:

probability(A,not B)+probability(B,not C) is greater or equal to probability(A,not C)

Bell found a set of propositions that violate this constraint according to quantum mechanics.

So it's not that anything travels faster than light. It's just that it's simply not true that some propositions are either true or false. This condition, if you will, "that something that could be true (has non-zero probability of happening) has become true" cannot be made into a signal.

Think how delicately all depends on the results being actually random: If Alice could decide what the outcome is going to be, her sequence of up, down, up, up, etc. would be read by Bob as the negative image of the message: down, up, down, down, etc.

Edited by joigus
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36 minutes ago, hoola said:

I have heard that is "how it works", but that doesn't explain the internal workings of the black box attributed to the idea.

What 'black box' are you referring to ?

Say I take a pair of gloves, and put one in one sealed box, and the other in another sealed box. I give you one box and a plane ticket to Australia, and the other box to Joigus. Neither of you knows which glove is in your box.
When you get to Australia, you open the box, and find a right-handed, or left-handed glove.
As soon as you've done that, you immediately know the handedness of the glove in Joigus' box, as they are correlated by pairing.

No information transferred, and the only 'black boxes' are the ones that held the gloves.
( this is a thought experiment; buy your own ticket to Australia )

Edited by MigL
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Is the glove analogy quite correct, though?  The objects in the boxes have no definite handedness until you open them, right?  If you open your box, you forced an ambidextrous glove to become a left-hand or RH glove by doing so.  And you will never be able to make the box create a specific handedness.  So no superluminal digital signal.

(Disclaimer: I understand very little of QT)

BTW, completely useless digression, but any glove can reverse handedness.  (Hint: easier with unlined rubber gloves). Topologically, any glove contains its own enantiomorph.

 

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2 hours ago, TheVat said:

Is the glove analogy quite correct, though? 

No it isn't correct because the gloves would need to be in an undefined state while in the boxes.
But correct enough to illustrate that there is no information transfer, superluminal or otherwise.

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I basically am asking if something could be added to the box, as a deliberate modification or addition to what is there, without excessive disturbance to the function of the box. 

Edited by hoola
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3 hours ago, hoola said:

I basically am asking if something could be added to the box, as a deliberate modification or addition to what is there, without excessive disturbance to the function of the box. 

There is no box. There isn’t a mechanism at play. As joigus has pointed out the correlation is in place all along.

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12 hours ago, TheVat said:

Is the glove analogy quite correct, though?

It is correct to describe classical gloves, the gloves we are familiar with.

10 hours ago, MigL said:

No it isn't correct because the gloves would need to be in an undefined state while in the boxes.

Exactly. It's not a property of ordinary gloves to be in a state that's neither left-handed, nor right-handed, but in a quantum superposition of both. That's what ordinary gloves can't do. A system that did this --hypothetically or actually--, as you well know, is called a Schrödinger cat. People call Schrödinger cats other kind of systems that are macroscopic, but keep quantum coherence. But I think there's a slight shift in meaning there, because ordinary cats (which are always either dead or alive) don't keep quantum coherence.

10 hours ago, MigL said:

But correct enough to illustrate that there is no information transfer, superluminal or otherwise.

Exactly. That was Bell's point in is paper Bertlemann's Sockets and the Nature of Reality. The point being: You don't need information transfer at a distance in order to have perfect distant correlations. You only need to prepare the system with those correlations built in.

5 hours ago, hoola said:

I basically am asking if something could be added to the box, as a deliberate modification or addition to what is there, without excessive disturbance to the function of the box. 

In what sense are you using the word "box"?

In science people talk about a black box when there's some internal mechanism we can't see, or we don't care about, except for its input/output workings.

You could call the evolution of the wave function a "black box" if you want. It all depends on what you mean by a "black box". When I said:

13 hours ago, joigus said:

The black box is in the mathematics of quantum mechanics.

what I meant is: You can't reproduce quantum behaviour by means of any classical and local internal switches, so to speak, that do the trick.

For example, MigL's gloves is a perfect example that illustrates that there doesn't have to be anything funny (non-local, superluminal) going on with one classical observable (handedness of a glove) and a pair of classical (non-quantum) systems (the gloves). John Bell provided a similar example that he called "Bertlemann's socks": One is pink, the other is green, or so I remember. What it illustrates is that perfect anti-correlation, or correlation between two distant things is not the problem.

The problem with quantum systems is evidenced when you consider at least 3 observables. And not just any observables; you have to pick them cleverly. Otherwise, you fall back to a range of variables where the classical explanation could work.

So let's make a pair of "quantum gloves."

Handedness: When one is R-handed, the other is L-handed

Colour: When one is B (black) the other is W (white)

Material: When one is N (nylon) the other is F (felt)

Whenever you take a look, the gloves are either RH or LH, either B or W, either N or F. But you're only allowed to take a look at any one of these properties at a time.

All of this happens only upon observation. If the system's not being observed, the quantum state allows you to be in so-called superposition states, in which the system is neither totally RH, nor totally LH, etc.

----------------------

Bell's Theorem

Bell's theorem is a very simple constriction on the probabilities of three independent assertions that are subject to classical logic (at all times, they're either true or not true.)

A: Possible outcomes: A is true | A is not true

B: Possible outcomes: B is true | B is not true

😄 Possible outcomes: C is true | C is not true

We can represent these outcomes as A, and A with a bar on top, etc. Like this:

image.png.3e33ed9d10cc4c3a9b51ea155ebb2469.png

The probability of A being true is the interior of the red circle. A not being true is the exterior. Etc.

Now, it's pretty clear (in images) that,

image.png.25434ea7a72de6b7e66bc678e4a9ef1d.png 

p(A,B-bar) being "probability of A being true and B being not true, etc.,

and, next to obvious* that,

image.png.ffe7c8e01e29a7e854b639c209202fae.png

This is what, quite "simply" quantum mechanics doesn't obey. There is this interesting case:

A = "the x projection of the particle's spin is up" (not A, or A-bar is read by substituting "is up" for "is down", etc.

B = "the y projection of the particle's spin is up", etc.

C = "the projection of the particle's spin along a direction 45º with respect to both x and y is up".

Then you use some so-called sigma-matrix algebra and voilá, Bell's theorem is violated. Experiments, BTW, confirm this within detector-noise tolerances. It's been checked upwards and backwards.

What's wrong? Nothing's wrong. It's simply not true that propositions A, B, and C all have a definite answer, true or not true while the system is evolving. It's all withing the very simple, transparent box of quantum mechanics. The tricky thing is "what happens to the quantum vectors when I perform a measurement?" But that's another story.

 

*Actually, not that obvious from the picture. I have a better proof elsewhere.

image.png

Edited by joigus
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the "box" are the algorithms that produce it. While the numbers are stored in an i file, still they are numbers, so they may respond to manipulations from real numbers.

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20 minutes ago, hoola said:

the "box" are the algorithms that produce it. While the numbers are stored in an i file, still they are numbers, so they may respond to manipulations from real numbers.

What algorithms? Numbers are stored?

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Seems like you're suggesting a random-number generator, not exactly an algorithm... That's precisely when you get into trouble with locality. Don't you see?

These "random-number generators" should agree to produce perfectly correlated random numbers at Alice's and Bob's position when asked the same question, and totally uncorrelated random numbers when asked different questions.

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On 9/9/2022 at 4:07 PM, joigus said:

No, there is nothing superluminal going on between both parts of the bipartite state in Bell's theorem.

All the correlations are initial. Quantum correlations were there when the state was prepared.

 

Could you clarify this part?

As I understand it, the quantum correlations of the entangled particles are indeterminate prior to the first observation rather than fixed at the moment of their preparation. They are neither-spin up nor spin-down unlike a pair of gloves that must have a fixed identity as either left handed or right handed prior to observation. The particles are in a state of superposition prior to the first observation.

Also, if particle A is observed to be in a spin-up position at position A, then the extremely remote particle B must be observed to be in the spin-down position even if a second observation at location B is made a nano second later.

This appears to be an example of one measurement having an instant affect on the other. How is that not a superluminal going on? Or properly called a non-local interaction?

On 9/10/2022 at 2:23 AM, hoola said:

I basically am asking if something could be added to the box, as a deliberate modification or addition to what is there, without excessive disturbance to the function of the box.

This can be accomplished with experiments known as “quantum teleportation” but the modifications can not be made deliberate.

For example, Alice can generate a pair of entangled electrons A and B and send electron B to Bob at a remote location while placing electron A in a “box”. She can then create another entangled pair of electrons C and D and direct electron D into the same box with A. Anton Zeilinger calls this a four-way or ABCD entanglement. Zeilinger is best known for his early experiments with quantum teleportation which is why he is called “Mr Beam”.

After the insertion of electron D into the box with electron A, Alice can then observe her remaining electron C. If electron C is spin up, the electron D that she put in the box is now spin down making its partner A spin-up and its away partner B that she sent to Bob spin down.

The overall observation is that the spin direction of the second particle she puts in the box will always be the same as the the spin direction of the particle at Bob’s location making it appear that she placed one particle in the box and it instantly appeared at Bob’s location. No particles have been physically teleported from one location to another but the quantum identity of the second particle placed in the box has been teleported to Bob’s location.

The modification can not be made deliberate because Alice has no way of knowing the random identity of any of the particles she generates prior to the experiment. If an observation is made of any one particle, none of the particles are allowed to remain in a superposition state and entanglement is lost..

 

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9 hours ago, bangstrom said:

As I understand it, the quantum correlations of the entangled particles are indeterminate prior to the first observation rather than fixed at the moment of their preparation.

You're confusing correlations between observables being there (and actually not changing at all during evolution) with observables being indeterminate. It's not the same thing. In the singlet state, correlations are very well defined, yet the projection of spin along any direction is expected to be zero on average. I said it before. It's about a couple of variables having zero expected value for each one of them, and yet being perfectly defined and with zero dispersion (no statistical variance, standard deviation, dispersion, as physicists say) for the sum of both. Schematically, if A and B are the respective projections of spin along a fixed axis for both particles respectively,

Average values of both:

\[ \left\langle A\right\rangle =0=\left\langle B\right\rangle \]

Average value of the sum:

\[ \left\langle A+B\right\rangle =0 \]

Dispersion of each:

\[ \sqrt{\left\langle A^{2}\right\rangle -\left\langle A\right\rangle ^{2}}=\sqrt{\left\langle A^{2}\right\rangle }=\sqrt{\frac{1}{4}}=\frac{1}{2} \]

But, (and here's the rub) dispersion of the sum of both:

\[ \sqrt{\left\langle A^{2}+2AB+B^{2}\right\rangle }=\sqrt{\frac{1}{4}+2\frac{-1}{4}+\frac{1}{4}}=0 \]

So, as I said earlier, each one of them is as indeterminate as it can be, but the quantity formed by the addition of both is sure zero every single time we measure.

Does that clarify the discussion?

45 minutes ago, joigus said:

I said it before. It's about a couple of variables having zero expected value for each one of them, and yet being perfectly defined and with zero dispersion (no statistical variance, standard deviation, dispersion, as physicists say) for the sum of both.

Sorry, I wasn't clear here. It's about a couple of variables (which have zero expected value for each one of them) having big dispersion for each one of them, while being dispersionless (zero dispersion) for the sum of both.

Dispersion is a measure of how "statistically spread" the results are.

Edited by joigus
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15 hours ago, joigus said:

So, as I said earlier, each one of them is as indeterminate as it can be, but the quantity formed by the addition of both is sure zero every single time we measure.

Does that clarify the discussion?

That answers my question concerning your statement about when correlations take place. You said, “All the correlations are initial. Quantum correlations were there when the state was prepared.” It was not clear from this when the correlations began.

If you are saying that the correlations are initiated at the instant when the first measurement is made and for both particles, that is something I can agree with..

My other question was about the timing of the correlation. If the measurement of one entangled particle instantly fixes the identity of its partner particle, no matter how far the distance, how can that not be considered to be a non-local interaction?

As I understand the Bell test, Einstein proposed the existence of a hidden variable that maintained a constant correlation between the two particles thus maintaining the appearance of locality.

Bell’s test was to identify if there was such a hidden variable and he found none suggesting that the correlation was truly non-local without the help of any hidden variable. Identifying a single identity of one particle instantly fixes the identity of the other at any distance and that is what I would call non-locality.
 

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11 minutes ago, bangstrom said:

If you are saying that the correlations are initiated at the instant when the first measurement is made and for both particles, that is something I can agree with..

Then you absolutely have missed the point of what's going on, and are still living in the confusion. This is what Murray Gell-Mann calls the "widespread foolishness associated with the EPR effect."

Go back to the example of the gloves that MigL was talking about. One glove goes to Australia and the other stays with me. I open the box and find out that it's LH. I thereby know immediately that hoola got the RH one. Would you think for a moment that one glove corresponds to the right hand and the other to the left hand because some "spooky action at a distance" has taken place between them? That's what's foolish to say. The gloves are perfectly anti-correlated just because the correlation was there from the beginning.

I can repeat the point over and over if you wish, but I can't make it any more clear.

The story of the argument is somewhat contorted, because Einstein thought of a different example, with position and momentum, and then David Bohm proposed one with spins. But you got the story wrong too.

That's for another post, though.

 

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On 9/9/2022 at 6:15 PM, joigus said:

So he could determine in principle that Alice has performed a measurement, but he wouldn't be able to tell which outcome Alice got until he made the measurement.

...if Bob could determine whether Alice has made a measurement, then Alice could send a message faster than light purely by choosing whether to perform measurements, if I'm understanding what you're saying correctly.

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I think you hould quote all of Joigus' post

On 9/9/2022 at 7:15 PM, joigus said:

Very fine point, but I think you're right. He may be able to devise a clever interference experiment though, to determine that someone's been messing with the state, because coherence has been broken. So he could determine in principle that Alice has performed a measurement, but he wouldn't be able to tell which outcome Alice got until he made the measurement.

But even if he could
What information, other than the collapse of a mathematical construct ( wave function ) of a model, would you be able to send ?

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