Undergrad Implications of the Delayed Choice Quantum Eraser

[Derek Potter]

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.

No, probability is given by the square of the magnitude of something called probability amplitude. Probability amplitude is a complex number. Probability amplitudes are added together like vectors (Pythagorus!) where two contributions arrive together. There is no change in the state that gives rise to the probability amplitude The result can be bigger than either or less than both. Hence interference.

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?

Yes.

Also, before, I was under the assumption that the results of D1 and D2 themselves exhibited interference patterns.

I thought the same thing at one time too, but I was wrong.

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.

Well, don't give up. A lot has happened since I grappled with Schrodingers cat at University. My own feeling is that we are almost there. I doubt whether things will happen overnight - one day there are 20 plausible interpretations, each one a bit unsatisfactory, the next day we have one complete and obvious picture. But it's likely, in my opinion, that we will very soon be able to constrain what form viable interpretations may take far tighter than the present free-for-all. I don't want to derail this thread by discussing it though, there's a lot to it. On the subject of which, a certain amount of discussion about "what goes on", i.e. interpretation, is tolerated on this forum, but generally anything that smells of philosophy is anathema and will get a thread terminated in less time than it takes for Schrodinger's cat to decohere.

 

[DrChinese]

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.

In QM, entanglement is a state. Is it "physical"? Hmmm. I guess it would call it physical but I get that you might interpret differently. No problem there.

Yes, it could be "merely" correlated to something, but remember that these are perfect correlations - a far more difficult measurement state to have occur. For there to be a correlation (in this case), there should definitely be a common cause somewhere. What is the common cause? Presumably, the cause should precede the perfect correlation. But that is not a requirement of QM, only of classical correlation.

Alice's bell state measurement is done after the other 2 photons are measured. Or before, doesn't matter. The other 2 photons can exist at any point in space time, including points nonlocal and/or non-overlapping in time with each other. And you get to decide whether to instruct Alice to even perform the bell state measurement, and when to do it. Alice has no way to even know what the outcome of the other measurement is (or will be, as the case may be). So the perfect correlations of processes outside of each others' light cones have a common cause of... what exactly?

And even if there is FTL physical collapse: what is collapsing, and when and where? And why would there be a perfect correlation between separately collapsed photons? So yes, I think there is plenty of mystery here.

 

[quantumfunction]

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.

I think that seems to be a problem in some cases. I think people start with the premise "This can't be true." So there must be an explanation that fits what they believe to be true. So they "demystify" these things but I don't see how that's possible.

What this experiment seems to be saying on it's face is that particles "know" what the position of other particles will be even in the future. So the particle at D0 behaves as a wave if the entangled pair hits D1 or D2 even after the particle has hit D0. If the particle hits D3 or D4 then which path information is known and the particle at D0 behaves like a particle.

So the obvious question is how does the particle at D0 know when which path information can or can't be known? I don't think it's something that needs to be "demystified" because that just means a person believes the experiment can't mean what it means so we have to explain it away or say it's too complicated to understand.

The same thing happens with Entanglement swapping delayed choice experiment.

The vertical axis represents time, moving into the future as you go up. They start with two pairs of entangled photons, which are sent into optical fibers. Two of these (one from each pair) go directly to detectors that record their polarizations roughly 35 ns after they were produced. The other two go into very long fibers, and are sent to a detector that either records the two original polarzations, or makes a joint measurement of the two together. If they measure the individual polarizations, the original pairs remain independent of one another, but if they make a joint measurement of the two, that entangles their states, meaning that the polarizations of the othertwo photons are now entangled with each other, and should be correlated.

Since these photons went into much longer fibers (104m vs. 7m), though, the entangling measurement is made after the two photons whose states are being entangled have had their polarizations measured– about 520 ns after they were produced.

In keeping with the silly jargon of the field, the two photons that are detected immediately (Photons 1 and 4) go to detectors that are imagined to be held by people named “Alice” and “Bob.” The two that are measured together to determine the entanglement (Photons 2 and 3) go to a third imaginary person named “Victor,” and it’s Victor’s measurement that determines everything.

So how did Alice and Bob's particles "know" whether Victor would entangle/not entangle after their particles have already been measured? Why isn't Alice and Bob's measurement independent of Victor's choice to entangle/not entangle?

These are the obvious questions on it's face that can't be easily explained away because in the end it really depends on which interpretation of QM you choose to accept.

Here's a couple of links:

http://scienceblogs.com/principles/2012/05/04/entangled-in-the-past-experime/

http://arstechnica.com/science/2012...cts-results-of-measurements-taken-beforehand/

This goes to things like is the wave function real or not. There's some Scientist even saying the wave function is real but a NON PHYSICAL Reality.

The wave-function is real but nonphysical: A view from counterfactual quantum cryptography

Counterfactual quantum cryptography (CQC) is used here as a tool to assess the status of the quantum state: Is it real/ontic (an objective state of Nature) or epistemic (a state of the observer's knowledge)? In contrast to recent approaches to wave function ontology, that are based on realist models of quantum theory, here we recast the question as a problem of communication between a sender (Bob), who uses interaction-free measurements, and a receiver (Alice), who observes an interference pattern in a Mach-Zehnder set-up. An advantage of our approach is that it allows us to define the concept of "physical", apart from "real". In instances of counterfactual quantum communication, reality is ascribed to the interaction-freely measured wave function (ψ) because Alice deterministically infers Bob's measurement. On the other hand, ψ does not correspond to the physical transmission of a particle because it produced no detection on Bob's apparatus. We therefore conclude that the wave function in this case (and by extension, generally) is real, but not physical. Characteristically for classical phenomena, the reality and physicality of objects are equivalent, whereas for quantum phenomena, the former is strictly weaker. As a concrete application of this idea, the nonphysical reality of the wavefunction is shown to be the basic nonclassical phenomenon that underlies the security of CQC.

http://arxiv.org/abs/1311.7127

There were other Scientist who also reached similar conclusions.

I think it all comes back to MWI and Everett's postulate on isolated systems. There's a global superposition of all possible states so you can't look at any observable state in this system as having an independent classical existence.

I think there's less need to try and "demystify" these things with MWI.

 

[Derek Potter]

In QM, entanglement is a state. Is it "physical"? Hmmm. I guess it would call it physical but I get that you might interpret differently. No problem there.

Entanglement can, of course, be described as a non-separable wavefunction. But a non-separable wavefunction can always be expanded as a superposition of separable states. I actually asked about this on this forum as I wasn't quite sure about the "always", but it turns out it's a theorem. Since superposition is a consequence of linearity, if we assume that it persists, there is no need to posulate a mysterious physical tie between the particles. To be quite clear about this, Bartlemann's socks are perfectly correlated with classical correlation. They were made as a pair and sent on their way. Alice and Bob's photons were made as a pair too, and were sent on their way. The difference is, the socks were sent as a mixed state |red>|blue> OR |blue>|red> but the photons are created (because of spatial symmetry) as a superposition of |H>|V> AND |V>|H>. |H> and |V> span the same state space as |a> and |a+90>, where a is an arbitrary angle, so the EPR correlation is maintained for just as long as the superposition does not collapse or otherwise decohere.

Yes, it could be "merely" correlated to something, but remember that these are perfect correlations - a far more difficult measurement state to have occur. For there to be a correlation (in this case), there should definitely be a common cause somewhere. What is the common cause? Presumably, the cause should precede the perfect correlation. But that is not a requirement of QM, only of classical correlation.
Alice's bell state measurement is done after the other 2 photons are measured. Or before, doesn't matter. The other 2 photons can exist at any point in space time, including points nonlocal and/or non-overlapping in time with each other. And you get to decide whether to instruct Alice to even perform the bell state measurement, and when to do it. Alice has no way to even know what the outcome of the other measurement is (or will be, as the case may be). So the perfect correlations of processes outside of each others' light cones have a common cause of... what exactly?

You are dragging me into discussing detail I am not sure of! Still, I am willing to bet that Victor cannot determine the entanglement until after Alice has told him which pairs to consider entangled and Bob has told him the detection results. It's only if you insist that the photons really were physically affected that the effect precedes the cause. Since the superposition interpretation of entanglement does not need this effect there is no requirement for a cause, common or otherwise.

And even if there is FTL physical collapse: what is collapsing, and when and where?

Collapse? FTL? Such things may go on in Copenhagen but they don't exist in my universe.

And why would there be a perfect correlation between separately collapsed photons?
So yes, I think there is plenty of mystery here.

No, just the need to be consistent. Before the infamous von Neumann cut everything is superposition, neither the photons nor the detector states collapse, the correlation emerges as an improper mixed state. After the cut you can treat it as a proper mixture. I would say "FAPP" but bhobba would probably say "because we can't tell the difference" - there is a subtle difference in the ontology. Your argument hinges on placing the cut at the first detection, effectively denying that the superposition persists and insisting on a collapse.

 

[Derek Potter]

I think there's less need to try and "demystify" these things with MWI.

In all the examples I know about, an MWI description of the system predicts the results without the slightest mystery. But there's no need to go to full-blown MWI, all that you need to do is make sure you place the "infamous" von Neumann cut late enough in the experiment that superposition can work its magic. You can even add a handful of particles, say 10⁹³ of them, bobbing along on the wavefunction if you want to get rid of all those dead cats, I mean all those embarrassing other worlds.

 

[DrChinese]

To be quite clear about this, Bartlemann's socks are perfectly correlated with classical correlation. They were made as a pair and sent on their way. Alice and Bob's photons were made as a pair too, and were sent on their way. The difference is, the socks were sent as a mixed state |red>|blue> OR |blue>|red> but the photons are created (because of spatial symmetry) as a superposition of |H>|V> AND |V>|H>. |H> and |V> span the same state space as |a> and |a+90>, where a is an arbitrary angle, so the EPR correlation is maintained for just as long as the superposition does not collapse or otherwise decohere..

Almost everything here is incorrect as it pertains to the Delay Choice Entanglement Swapping (DCES, which is completely analogous to the DCQE in theoretical points). Bertlmann's socks IS classical (and has no bearing here anyway). But the entangled photon pair in DCES is not, and not only were they NOT made as a pair - they need never have existed at the same time. The EPR correlation does not even exist at the time the photons are measured and the related "collapse" occurs. That is done later.

I think my point in all this is: you are selling a naive version of these experiments. But they are complicated and touch on the outer edges of quantum weirdness. You deny that any collapse has occurred when measurement has taken place, yet in a different context you could say that is absolutely has because the outcome of an observation on entangled twins can be predicted with certainty. That does not imply an ongoing superposition at all!

What I am saying mimics QM itself: know the full context, you know the probabilities. The context need not be local or in a particular causal sequence. Why it works out that way is the mystery.

 

[DrChinese]

I think that seems to be a problem in some cases. I think people start with the premise "This can't be true." So there must be an explanation that fits what they believe to be true. So they "demystify" these things but I don't see how that's possible.
...
These are the obvious questions on it's face that can't be easily explained away because in the end it really depends on which interpretation of QM you choose to accept.
...
I think there's less need to try and "demystify" these things with MWI.

Yes, the determination of which thing "can't be true" drives one's interpretation.

I don't really have an issue with the many worlds of MWI if it answers some good questions. I just don't see how you get very far with that with the Delayed Choice experiments, because the choice of context is delayed past the point where I think there should have been a splitting. And some of the split off worlds later become impossible worlds (because of perfect correlations, which won't support imperfect permutations). But that's just me. :)

 

[Derek Potter]

Almost everything here is incorrect as it pertains to the Delay Choice Entanglement Swapping (DCES, which is completely analogous to the DCQE in theoretical points).

Did you not notice the term "EPR" towards the end of the paragraph?

You deny that any collapse has occurred when measurement has taken place, yet in a different context you could say that is absolutely has because the outcome of an observation on entangled twins can be predicted with certainty.
That does not imply an ongoing superposition at all!

Are you serious? There is perfect correlation in each component state. Nothing else is needed except normal measurement theory.

 

[Kansas_Cowboy]

No, probability is given by the square of the magnitude of something called probability amplitude. Probability amplitude is a complex number. Probability amplitudes are added together like vectors (Pythagorus!) where two contributions arrive together. There is no change in the state that gives rise to the probability amplitude The result can be bigger than either or less than both. Hence interference.

I thought the same thing at one time too, but I was wrong.

But isn't adding the probability amplitudes together a representation of this interaction built into the equation? I'm not implying anything like bits of one wave colliding with the bits of other waves as you mentioned previously. I'm making no assumption as to what this interaction actually entails, merely asserting that it must exist.

Also, I'm a tad confused. If I understand you correctly, you're saying that D1 and D2 results don't show interference? That only the signal photons associated with D1 and D2 produce interference patterns on D0? What then are the results of D1 and D2?

 

[Derek Potter]

Yes, the determination of which thing "can't be true" drives one's interpretation.

I don't really have an issue with the many worlds of MWI if it answers some good questions. I just don't see how you get very far with that with the Delayed Choice experiments, because the choice of context is delayed past the point where I think there should have been a splitting. And some of the split off worlds later become impossible worlds (because of perfect correlations, which won't support imperfect permutations). But that's just me. :)

In MWI the choice of context does not *cause* anything. With adequate fine-graining all the worlds exist "from the beginning". We have done to death the issue of "splitting". You can define MWI as "the silly popularist picture of parallel universes that split whenever someone makes an observation" or as "entangled states of observer and system, interpreted as relative states and augmented by decoherence-based measurement theory". I prefer the definition that will be lost on the hoi polloi but not for that reason. (I am not a snob, some of my best friends are common).

 

[Derek Potter]

But isn't adding the probability amplitudes together a representation of this interaction built into the equation? I'm not implying anything like bits of one wave colliding with the bits of other waves as you mentioned previously. I'm making no assumption as to what this interaction actually entails, merely asserting that it must exist.

The two states don't affect each other. The detector interacts with the sum. That's no different from a TV and a radio blaring in the same room. They don't affect each other but your ear has to deal with the total racket.

Also, I'm a tad confused. If I understand you correctly, you're saying that D1 and D2 results don't show interference? That only the signal photons associated with D1 and D2 produce interference patterns on D0? What then are the results of D1 and D2?

Yes, at D1 and D2, you just get a broad lobe, no interference pattern.

 

[DrChinese]

Are you serious? There is perfect correlation in each component state. Nothing else is needed except normal measurement theory.

Let's see. I measure a photon of entangled pair A at 87.3 degrees. My friend, far away, measures a photon of entangled pair B at 87.3 degrees.

How are those still in a superposition? My photon and my friend's are already measured and the values are known! And how is there any correlation now between these at this odd choice of angle - or any angle we decide upon - if the decision to retroactively entangle these 2 distant particles via swapping is made at a later time? There was no "perfect correlation" until later.

 

[quantumfunction]

Yes, the determination of which thing "can't be true" drives one's interpretation.

I don't really have an issue with the many worlds of MWI if it answers some good questions. I just don't see how you get very far with that with the Delayed Choice experiments, because the choice of context is delayed past the point where I think there should have been a splitting. And some of the split off worlds later become impossible worlds (because of perfect correlations, which won't support imperfect permutations). But that's just me. :)

I think you make a some good points and I think if you support MWI, you have to take into account that what information can be known about the system in the environment seems to mean something.

You ask an obvious question because if you look at the entanglement swapping experiment, you have to ask why wasn't there a split when Bob and Alice's particles were measured? MWI can't answer that question at least in the context of a physical interaction. There's no reason why Alice and Bob's measurements should be dependent on Victor's choice in the future.

It's like the particles are delaying their choice on whether they will be entangled/not entangled until Victor decides what he's going to do even after their particles have been measured.

It looks like whether the information about the state of the particle can be known by the environment is even more important than measurement. So the state of the particle seems to be in limbo until Victor makes a choice even after a measurement has already occurred.

I personally like the idea of the wave function as a non physical reality. So you can define physical apart from real.

So the superposition of states only become physical when information about the system can be known in the environment of the observable state of an isolated system. This begs the question, what's physical? Does an observable state only appear real to observers in a local environment?

Let's just assume the wave function is a non physical reality. What if the "universe" is simply a physical isolated system and it's wave function evolves all possible states of this isolated system. So what we call physical reality is just a projection of states of this isolated system. So we could be holograms, phantasms or whatever you want to call it because this physical isolated system could never physically occupy all of space that's expanding faster than light.

Another question that would need to be asked is if this physical isolated system has a finite configuration or arrangement it can be in. Tegmark and others seems to think it's finite so we can be in some infinite loop of existence as the same and similar states keep occurring ad infinitum.

Just a thought

 

[Gaz]

Well I don't know much but I know this is wrong

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.

Using V and H polarizer's can be explained by both QM and classical physics as there would be no interference from v polarized and h polarized em wave so Is no evidence for either.

The which path information is what is supposed to collapse the probability wave. If a photon registers at D3 or D4 then you know which path it came from and the wave collapses. I just can't get my head around QM.

 

[DrChinese]

Using V and H polarizer's can be explained by both QM and classical physics as there would be no interference from v polarized and h polarized em wave so Is no evidence for either.

True enough. (Although I don't know how you think my quoted text had something misstated.)

My point was that you can learn which path information from a quantum particle without otherwise altering it. The relative orientation of the polarizers should not matter to the outcome if a particle only goes through one slit or the other. Obviously, the relative orientation DOES matter.

 

[Gaz]

Sorry Like I said I don't know much about it =)

 

[Derek Potter]

Let's see. I measure a photon of entangled pair A at 87.3 degrees. My friend, far away, measures a photon of entangled pair B at 87.3 degrees.
How are those still in a superposition? My photon and my friend's are already measured and the values are known!

Sorry but in MWI you don't know the value because there is no single value to know. That's why it's called "Many".

The superposition is very simple. The initial two photon state was .707|H>_you|V>_friend +.707|V>_you|H>_friend (anticorrelation). H and V are the possible outcomes in the 87.3 degree basis. After interaction the joint detector state is .707|1>_D1|0>_D2 + .707|0>_D1|1>_D2. In a two-photon experiment that is the end of the matter - ordinary measurement theory tells us that the superposition looks like a mixture.

 

[Derek Potter]

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?

The detection at D1 or D2 is also AFTER the photon is detected at D0

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.

Huh? I didn't say anything like that, I said "If you look at the ray paths, D1 and D2 can only see one slit, D3 and D4 see both." It's simple optics, D3 sees a reflection of slit A in BSA, D1 sees slit A through BSA but reflected by MA and BSC. It also sees slit B through BSB and reflected by MB but through BSC. Nothing whatsoever about photons knowing where they're going to hit.

 

[Kansas_Cowboy]

The two states don't affect each other. The detector interacts with the sum. That's no different from a TV and a radio blaring in the same room. They don't affect each other but your ear has to deal with the total racket.

Yes, at D1 and D2, you just get a broad lobe, no interference pattern.

I still feel like that is a misrepresentation. At the end of the day, a single photon hits the detector. The detector interacts with a single photon. It is the photon's position upon reaching the detector that is determined by the sum of probabilities. Thus, the probabilities are acting upon the photon's final position, not upon the detector. Can we agree when I phrase it like this?

And on the second point, after some thought, it makes sense. Not only would the timing likely differ slightly for the idler photons to reach D1 or D2 depending on the slit, but from the diagram at least, it appears that they are angled such that they ultimately reach the detectors from the same point of the beam splitters regardless of slit.

 

[berkeman]

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