Implications of the Delayed Choice Quantum Eraser

[Kansas_Cowboy]

My mind was blown upon discovering this experiment. Subsequent attempts at putting my brain back together have all failed miserably. All posts trying to demystify the experiment have either appeared flawed or were too complex for my primitive liberal arts brain to understand. Now I fear such brain contusions may simply be a side effect of studying quantum physics in general, but I'm hoping you guys can help me out anyway.

Basically, my understanding of the experiment leads me to the uncanny conclusion that the behavior of these photons is dependent on our access to information concerning which specific slot they initially pass through. When this information is discernible, the correlating photons act like particles. Yet when this information is unavailable, the correlating photons produce interference patterns as if they were waves. Not only that, but entangled pairs display the same behavior even though one reaches its detector before the other one even reaches the beam splitter, the results of which determine whether or not such information will be available. And SOMEHOW, I find this latter prospect to be much more reasonable and understandable than the first.

Is this understanding correct? Should I even bother looking for the remaining bits of brain I have yet to recover post-explosion?

 

[Kansas_Cowboy]

One guy was like, "The truth is actually quite obvious and less mysterious that often presented. It is of the "eating your cake and having it" kind. You cannot detect a photon just after it has passed the slits and still expect the same photon to reach the screen. At the very least your efforts will disburb/deflecting the photons. Therefore, by attempting to detect photons at the slits, you have introduced a disturbance which perturbs your interference pattern!"

However, this seems like a misunderstanding of the experiment. All of the idler photons are eventually detected. It just so happens that if by chance they reach D3 or D4, then we may indirectly infer which slot they went through. If they instead pass through the initial beam splitter and reach D1 or D2, then the information is lost. If mere detection produces a disturbance interfering with the interference pattern, then one would not expect to see an interference pattern anywhere in this experiment.

 

[bhobba]

Without going into the details its not nearly as mind blowing as all that - its simply that decoherence, while usually irreversible, can be undone in simple circumstances.

But if you want to understand it there is no substitute of slogging through the details including the math. Sadly there is no lay way of getting to the bottom of this experiment - you must delve into the details of QM.

Its examined in chapter 20 here:
http://quantum.phys.cmu.edu/CQT/index.html

But to understand chapter 20 you need the time and patience to go through the earlier chapters. Even though it contains math this book has been designed with a minimum of it to be accessible to as wide an audience as possible but it will still require your close attention.

Thanks
Bill

 

[Kansas_Cowboy]

Without going into the details its not nearly as mind blowing as all that - its simply that decoherence, while usually irreversible, can be undone in simple circumstances.

But if you want to understand it there is no substitute of slogging through the details including the math. Sadly there is no lay way of getting to the bottom of this experiment - you must delve into the details of QM.

Its examined in chapter 20 here:
http://quantum.phys.cmu.edu/CQT/index.html

But to understand chapter 20 you need the time and patience to go through the earlier chapters. Even though it contains math this book has been designed with a minimum of it to be accessible to as wide an audience as possible but it will still require your close attention.

Thanks
Bill

I assume by decoherence, you're referring to the collapse of the wave function? Is that correct?

Also, I could be wrong, but that chapter seemed to deal largely with refuting retrocausality. I'm particularly interested in why the results differ between D1/D2 and D3/D4. Could you provide any insight on that issue? Is there anything wrong with the following simple statement?: In this experiment, photons exhibit particle-like behavior when information is available regarding the specific slit through which they first passed and wave-like behavior when this information is unavailable?

Perhaps I'm asking too much. Perhaps this aspect of quantum physics must necessarily remain esoteric, a golden idol of knowledge hidden deep within an ancient temple of complex mathematics. But it would be great if any of you Indiana Jones's could break into the temple, grab the idol, get out while avoiding all the complex quantum math booby-traps, and fill me in on the escapade. The math must represent something after all.

 

[bhobba]

I assume by decoherence, you're referring to the collapse of the wave function? Is that correct?

Yes and no - its a subtle issue. But at a lay level you can say collapse is undone.

Could you provide any insight on that issue?

I thought it addressed that issue.

Is there anything wrong with the following simple statement?: In this experiment, photons exhibit particle-like behavior when information is available regarding the specific slit through which they first passed and wave-like behavior when this information is unavailable?

This wave particle thing is basically a myth:
http://arxiv.org/abs/quant-ph/0609163

Perhaps I'm asking too much.

Things are as they are. If you want to understand how a transistor radio works you have to understand how transistors work. If you want to understand the quantum eraser you must understand QM. That will take time and effort. There is some things in QM that can be explained in lay terms - however the eraser experiment isn't one of them. Even when you know QM it requires effort to get to grips with it.

Thanks
Bill

 

[Derek Potter]

Perhaps I'm asking too much. Perhaps this aspect of quantum physics must necessarily remain esoteric, a golden idol of knowledge hidden deep within an ancient temple of complex mathematics. But it would be great if any of you Indiana Jones's could break into the temple, grab the idol, get out while avoiding all the complex quantum math booby-traps, and fill me in on the escapade. The math must represent something after all.

No, it's extremely simple. The system remains in a superposition of all possible outcomes until after both photons have been detected. In the language of Schrödinger's Cat the system is in a state of [D0 & D1], [D0 & D2], [D0 & D3], [D0 & D4] at the same time. Each outcome has a weighting factor according to x. When this superposition is resolved by observation, one of those four is observed with the correct probability. That's all there is to it.

 

[Kansas_Cowboy]

No, it's extremely simple. The system remains in a superposition of all possible outcomes until after both photons have been detected. In the language of Schrödinger's Cat the system is in a state of [D0 & D1], [D0 & D2], [D0 & D3], [D0 & D4] at the same time. Each outcome has a weighting factor according to x. When this superposition is resolved by observation, one of those four is observed with the correct probability. That's all there is to it.

Thanks, Derek. If I understand correctly, this solves the mystery of retrocausality.

I'm also wondering why the results then differ between D1/D2 and D3/D4 in the way they do. Is this something that scientists simply haven't been able to explain yet, or is there some rationale? Perhaps something to do with the photons' interactions with beam splitters or mirrors?

 

[Derek Potter]

Thanks, Derek. If I understand correctly, this solves the mystery of retrocausality.
I'm also wondering why the results then differ between D1/D2 and D3/D4 in the way they do. Is this something that scientists simply haven't been able to explain yet, or is there some rationale? Perhaps something to do with the photons' interactions with beam splitters or mirrors?

If you look at the ray paths, D1 and D2 can only see one slit, D3 and D4 see both. It's as simple as that.

 

[DrChinese]

You cannot detect a photon just after it has passed the slits and still expect the same photon to reach the screen. At the very least your efforts will disburb/deflecting the photons. Therefore, by attempting to detect photons at the slits, you have introduced a disturbance which perturbs your interference pattern!"

As you pointed out, this is incorrect. As a matter of fact, you can determine which slit a photon goes through and it still reach the screen. One way to do that is to place a V polarizer at one slit and an H polarizer at the other. The interference pattern will disappear. On the other hand, if both polarizers are V, there will be an interference pattern.

 

[DrChinese]

Thanks, Derek. If I understand correctly, this solves the mystery of retrocausality.

Unfortunately, it does not. It is not clear why delayed choice experiments seem to have a retrocausal component.

A different delayed choice experiment shows: you can observe perfect correlations with a pair of entangled photons (ie observe both at any angle and the result will match the entangled state statistics). The punch line is that the photons are entangled AFTER they are detected, and the photons were never in a common light cone.

http://arxiv.org/abs/quant-ph/0201134

See page 5, where the delayed choice version is discussed:

"A seemingly paradoxical situation arises — as suggested by Peres [4] — when Alice’s Bellstate analysis is delayed long after Bob’s measurements. This seems paradoxical, because Alice’s measurement projects photons 0 and 3 into an entangled state after they have been measured. Nevertheless, quantum mechanics predicts the same correlations. Remarkably, Alice is even free to choose the kind of measurement she wants to perform on photons 1 and 2. Instead of a Bell-state measurement she could also measure the polarizations of these photons individually. Thus depending on Alice’s later measurement, Bob’s earlier results either indicate that photons 0 and 3 were entangled or photons 0 and 1 and photons 2 and 3. This means that the physical interpretation of his results depends on Alice’s later decision.

"Such a delayed-choice experiment was performed by including two 10 m optical fiber delays for both outputs of the BSA. In this case photons 1 and 2 hit the detectors delayed by about 50 ns. As shown in Fig. 3, the observed fidelity of the entanglement of photon 0 and photon 3 matches the fidelity in the non-delayed case within experimental errors. Therefore, this result indicate [sic] that the time ordering of the detection events has no influence on the results and strengthens the argument of A. Peres [4]: this paradox does not arise if the correctness of quantum mechanics is firmly believed."

 

[Derek Potter]

Unfortunately, it does not. It is not clear why delayed choice experiments seem to have a retrocausal component.

Not clear to whom? It seems clear to me that the appearence is due to imposing definiteness on observations. Keep everything in superposition and the paradoxes go away.

I'll wade through the entanglement swapping paper some time as entanglement swapping is rather new to me and keeping track of a four-photon state is a bit taxing to my poor brain. But I'd be utterly amazed if the same approach - no collapse, not even at observation - fails here at last, having successfully accounted for EPR and DCQE.

 

[bhobba]

Not clear to whom? It seems clear to me that the appearence is due to imposing definiteness on observations. Keep everything in superposition and the paradoxes go away.

In the early days of QM Von Neumann showed that's not possible - the Von Neumann cut must occur - but can be placed anywhere.

There are outs such as MW and Consistent Histories but without one of those outs its unavoidable.

If you don't want it you must clearly state what your out is and show it actually is an out.

Thanks
Bill

 

[Derek Potter]

In the early days of QM Von Neumann showed that's not possible - the Von Neumann cut must occur - but can be placed anywhere.
There are outs such as MW and Consistent Histories but without one of those outs its unavoidable.
If you don't want it you must clearly state what your out is and show it actually is an out.

Not really. The onus is on proponents of "cut" interpretations to say why they want to have a cut at all.
All my picture says is that the cut, if any, can be placed after the idler photon has been detected and this is sufficient to avoid paradox.

 

[bhobba]

Not really. The onus is on proponents of "cut" interpretations to say why they want to have a cut at all.

I disagree. The onus is on the no cut idea to show how it gets an outcome. All decoherence does is have a mixed state. That doesn't have an outcome without some other assumption.

Consider the mixed state 1/2 |a><a| + 1/2 |b><b|. What's its outcome?

Thanks
Bill

 

[Derek Potter]

I disagree. The onus is on the no cut idea to show how it gets an outcome. All decoherence does is have a mixed state. That doesn't have an outcome without some other assumption.
Consider the mixed state 1/2 |a><a| + 1/2 |b><b|. What's its outcome?

Whoah there! I do not want to confuse the already-exploded OP's brain with a review of all conceivable classes of interpretation. There is, as you know, an ongoing thread that I started in order to nail down the outcome problem. Let's discuss it there.
You can have a quantum/classical cut if you like - just don't place it too early in the experiment.

 

[jerromyjon]

I'm also wondering why the results then differ between D1/D2 and D3/D4 in the way they do.

Do you mean the π phase shift? That is exactly what I want to know.

 

[Derek Potter]

If you look at the ray paths, D1 and D2 can only see one slit, D3 and D4 see both. It's as simple as that.

Oops, wrong numbering, it's the other way round. Sorry.

 

[Kansas_Cowboy]

If you look at the ray paths, D3 and D4 can only see one slit, D1 and D2 see both. It's as simple as that. (fixed)

But none of the detectors truly see anything. They simply detect the photons. The experiment is setup so as to not interfere with the photons at the point in which they pass through the slits. Instead, this information is provided implicitly when the idler photons bounce off the initial beam splitter to reach D3 or D4, and unavailable if they happen to pass through. Correct?

 

[Kansas_Cowboy]

Do you mean the π phase shift? That is exactly what I want to know.

So is it simply a mystery? I would be ecstatic if I could get a simple "we don't know" as an answer to my question. This would allow me to stop scratching my head and leave it to greater minds than mine to scratch theirs.

Here's a quote from one of Richard Feynman's lectures in reference to the classic double slit experiment, "We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by "explaining" how it works. We will just
tell you how it works."

Now this was a very intelligent man, but I assume much progress has been made since he died. So I must ask, all of the answers that people are providing here, all of the answers produced in scientific papers thus far...Are they essentially just explaining how it works, explaining merely what occurs in the experiment? Or do they truly solve the mystery?

 

[Derek Potter]

So is it simply a mystery?

No, it's not a mystery. jerrymyjon asked you whether you meant the fact that the D0/D1 pattern is complimentary to the D0/D2 pattern, see figs 3 and 4 of the Kim paper.. He doesn't understand why they are different but that does not mean that nobody knows! I could work out the details and show you but it's tedious and really has nothing to do with the questions you asked at the beginning.

Feynman's reference to mystery did not mean that nobody knew how to explain phenomena with quantum mechanics, it meant that nobody knew why the world is quantum. Suppose the Lizard People are actually quite benign and are making sure that the Matrix simulation that we live in is self-consistent. What constraints does that place on our experience of physics? Must it be Newton's classical world with his Laws of Motion? Or must it be the magical world of Harry Potter and Hogwarts? Or is the quantum world the only possible self-consistent one? QM clearly steps outside the paradigm of classical physics and, being physics, it doesn't find an underlying, more fundamental science to stand on. Biology has chemistry and chemistry has physics but QM is pretty well on its own. To date no-one can provide a neat and tidy underlying picture that explains why it is what it is. But we do know what it is even if we don't know why. And we have no difficulty (in principle) in explaining quantum phenomena within that framework.

 

[Derek Potter]

But none of the detectors truly see anything. They simply detect the photons.

What is the difference between seeing a slit and detecting photons from a slit?

The experiment is setup so as to not interfere with the photons at the point in which they pass through the slits. Instead, this information is provided implicitly when the idler photons bounce off the initial beam splitter to reach D3 or D4, and unavailable if they happen to pass through. Correct?

If photons behaved ballistically then you would be right. But they don't and saying they "happen to pass through" is an interpretive assumption that they do. If you make that assumption then you will run into huge problems like retrocausality and so on. Quantum mechanically the probability amplitude (~wave function for our purposes) both bounces off and passes through the beam splitter. As I have said, follow the possibilities through the apparatus, don't assume anything is either/or but keep it all in superposition until the final reckoning.
You can couch the "which-path" information idea in quantum mechanical terms with complete rigour. But saying that "the interference is restored when the information is erased" needs to be put in those terms otherwise it becomes yet another "Gee-wizz isn't quantum mechanics weird?" vibe which we can do without.

 

[Kansas_Cowboy]

What is the difference between seeing a slit and detecting photons from a slit?

If photons behaved ballistically then you would be right. But they don't and saying they "happen to pass through" is an interpretive assumption that they do. If you make that assumption then you will run into huge problems like retrocausality and so on. Quantum mechanically the probability amplitude (~wave function for our purposes) both bounces off and passes through the beam splitter. As I have said, follow the possibilities through the apparatus, don't assume anything is either/or but keep it all in superposition until the final reckoning.
You can couch the "which-path" information idea in quantum mechanical terms with complete rigour. But saying that "the interference is restored when the information is erased" needs to be put in those terms otherwise it becomes yet another "Gee-wizz isn't quantum mechanics weird?" vibe which we can do without.

So it's the interaction between all of the possibilities that produce interference patterns? D1 and D2 include possibilities from both slits resulting in the interference pattern, while the possibilities relevant to D3 and D4 include only one slit, which then results in the apparent particle like behavior? Is this a fair characterization?

 

[Derek Potter]

So it's the interaction between all of the possibilities that produce interference patterns? D1 and D2 include possibilities from both slits resulting in the interference pattern, while the possibilities relevant to D3 and D4 include only one slit, which then results in the apparent particle like behavior? Is this a fair characterization?

Yes though I'd query a couple of the terms you use, not because I wish to be pedantic but to avoid any possible confusion.

1 I don't think interaction is a good word to use for interference. The waves are simply passing through each other. A true interaction would mean something in one "wave" collided with something in the other producing debris or altering the paths of the waves.

2 Possibilities don't do anything except happen - possibly :) It is of course the probability amplitudes that add together (bearing in mind they are complex numbers) and actual probabilities emerge via the usual Rules of Quantum Mechanics.

Note that it's detections by D0 and D1 at the same time that shows the interference pattern: there is no interference pattern actually at D0, nor at D1, so the idea of ordinary waves is misleading. (And as an entirely different matter, it's probably wrong for massless spin-1 entities like photons, for extremely deep reasons that I have not got a clue about). However, a complex number that represents the final probability doesn't have to live in real space, it's just a number.

3 Finally, I do not agree that the two patterns, one showing interference fringes and the other not, should be characterized as wave-like and particle-like. They are both wave-like patterns, one of a wave which has passed through two slits, the other of a wave that has only passed through one. To me, the term "particle-like" suggests a small compact object bouncing around. If that happens at all, it happens in the detector and is irrelevant. Unfortunately Kim et al use these terms and it is hard to buck the trend.

 

[DrChinese]

Not clear to whom? It seems clear to me that the appearence is due to imposing definiteness on observations. Keep everything in superposition and the paradoxes go away.

I'll wade through the entanglement swapping paper some time as entanglement swapping is rather new to me and keeping track of a four-photon state is a bit taxing to my poor brain. But I'd be utterly amazed if the same approach - no collapse, not even at observation - fails here at last, having successfully accounted for EPR and DCQE.

You might take the time to learn something new. The reason I posted the link is because DCQE experiment discussions quickly devolve to issues of comprehending the details of the setup. That gets pretty complicated, and I see from recent posts that the thing is happening here.

The DCES reference is easier to follow: Bell test violation from pairs of photons which are entangled after they are detected. So the question is how can you entangle something that no longer exists? You can talk about appearances, but a little examination of the experiment will show it lays out the issues you are discussing without the baggage you are tossing around.

Or you can ignore it, that is the more common route anyway.

 

[DrChinese]

So is it simply a mystery? I would be ecstatic if I could get a simple "we don't know" as an answer to my question. This would allow me to stop scratching my head and leave it to greater minds than mine to scratch theirs.

Here's a quote from one of Richard Feynman's lectures in reference to the classic double slit experiment, "We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by "explaining" how it works. We will just
tell you how it works."

Now this was a very intelligent man, but I assume much progress has been made since he died. So I must ask, all of the answers that people are providing here, all of the answers produced in scientific papers thus far...Are they essentially just explaining how it works, explaining merely what occurs in the experiment? Or do they truly solve the mystery?

The mystery is as Feynman says: QM describes the results to expect, but no one can tell you much deeper than that. We know some of the things that cannot be correct, but the underlying mechanisms rate a big fat "we don't know".

 

[DrChinese]

One difference between quantum probabilities and classical probabilities is that quantum probabilities can cancel each other out (classical do not). This side of interference between paths (histories) leads to the distinctive interference patterns. Only one of the paths is actually realized (randomly as anyone can best tell), but its likelihood is a function of all of the paths.

And the probabilities are controlled by the entire context of a setup. A quantum context can have past components, future components, local components and nonlocal components. Obviously, this too is different than a classical setup. We see this in the delayed choice type experiments.

 

[Kansas_Cowboy]

1 I don't think interaction is a good word to use for interference. The waves are simply passing through each other. A true interaction would mean something in one "wave" collided with something in the other producing debris or altering the paths of the waves.

2 ...Note that it's detections by D0 and D1 at the same time that shows the interference pattern: there is no interference pattern actually at D0, nor at D1, so the idea of ordinary waves is misleading.

Alright, I'm with you on three. Just a couple things on one and two.

First off, I'm not sure of a better word to use. Perhaps it is not an interaction in the classical sense, but it is the various possibilities together which result in the interference pattern. As DrChinese wrote, "Quantum probabilities can cancel each other out" with this feature of QM resulting in the interference patterns of these types of experiments. If the probabilities had no influence on each other, then the interference patterns couldn't exist. Therefore, as per my understanding at least, they must somehow interact.

Also, could you elaborate on the bit of quote I left for #2? As I understand, D0 doesn't exhibit the regular interference pattern when you take all results into account. When you look at the results of the signal photons associated with D1 and D2 hits, then you get the interference pattern. Whereas the signal photons associated with D3 and D4 lack the interference pattern. Is this correct? Also, before, I was under the assumption that the results of D1 and D2 themselves exhibited interference patterns.

The mystery is as Feynman says: QM describes the results to expect, but no one can tell you much deeper than that. We know some of the things that cannot be correct, but the underlying mechanisms rate a big fat "we don't know".

Interesting. Do you think we will ever know?

Personally, I think it could be impossible. No matter how clever the experiment we devise, it seems that we'll merely be validating our equations. What actually happens in the interim, the period between initiation of some phase of an experiment and the results observed, the actual physical manifestation of our equations and the underlying mechanisms of such manifestations...I fear this knowledge is forever beyond the grasp of the human mind as it has evolved.

 

[jerromyjon]

As I understand, D0 doesn't exhibit the regular interference pattern when you take all results into account.

Yes, it does. Only when the entangled photon is detected by D1 or D2 then you get interference patterns at D0 from the idler photon. When D3 or D4 gets a hit AFTER the photon is detected at D0, then you do not get interference at D0. Crazy, huh?

I think that is why Derek Potter likes to refer to the photons as "seeing the path they are going to take" because it is a way to rationalize what occurs. There is no physical evidence that the photons know where they are going to hit, only the logical implication that is contradicted by normal reality.

 

[Derek Potter]

You might take the time to learn something new. The reason I posted the link is because DCQE experiment discussions quickly devolve to issues of comprehending the details of the setup. That gets pretty complicated, and I see from recent posts that the thing is happening here.

That is what I said. I will take the time to learn about entanglement swapping. It it's what it looks like then the experiment is much simpler to describe than the Kim setup but I'm not going to be pressured into attempting an explanation until I am sure exactly what it is that I'm explaining.

The DCES reference is easier to follow: Bell test violation from pairs of photons which are entangled after they are detected. So the question is how can you entangle something that no longer exists?

Clearly you cannot if entanglement is a physical state that is mysteriously imposed on the photons. Clearly there is no difficulty at all if it is merely a correlation which is brought about by Alice telling Victor which pairs are to be considered to be correlated.

You can talk about appearances, but a little examination of the experiment will show it lays out the issues you are discussing without the baggage you are tossing around.

I have no idea what you mean by tossing baggage around. I travel light.

Or you can ignore it, that is the more common route anyway.

Yes, ignoring a problem is often much easier than resolving it. But we don't want to do that. Do we?

 

[jerromyjon]

I have no idea what you mean by tossing baggage around. I travel light.

Amen to that!

Yes, ignoring a problem is often much easier than resolving it. But we don't want to do that. Do we?

Depends who you ask I imagine. You seem like me, committed to finding an acceptable understanding why things are, rather than being content with simply how they are.