Delayed choice and information erasure

[cesiumfrog]

using spontaneous down conversion for creating entangled photons. This is a process stimulated by vacuum fluctuations just like spontaneous emission and therefore the photons are emitted at random times

Of course, thanks, that really clears up one question. But it does raise another question..

let's say we start with a single [pump] photon, sent through a down converter. [..] Here there is no issue of incoherence since initially there is a single photon.

But this isn't it. Spontaneous down conversion implies that the pump photon excites the crystal to a higher state, with some statistical life-time (which is presumably long compared to the period from the pump photon's frequency). Think nuclear decay. So however short the pump beam is on, the signal/idler photons are not in any specific phase with it (and of course, you get a superposition of all the times when the crystal's state could have decayed).

Spontaneous parametric down conversion has even been described as amplifying the vacuum fluctuations. There is another technique, just called parametric down conversion. We still have the pump beam to excite the crystal into the special state. But there is also a second supplied beam (I'll call it the tickler beam) that is basically intended to replace the random vacuum fluctuations in the job of stimulating the crystal's state to decay. The theory is that this stimulation will cause the crystal to release a pair of photons, one of which amplifies the tickler beam (same concept as gain in a laser, and so this new idler photon is presumably identical to one of the stimulating tickler beam photons, in every way), and the other of which we'll call the signal photon (which must be in phase with the emitted idler photon).

I'll have to research this topic further, but the suggestion is obvious: let the pump and stimulating tickler beams have low intensity, and wait for events where a signal photon is detected (noting that at the same time a pair of identical tickler beam photons should also be detected). In such events the signal photon is expected to produce interference (since all possible paths of the signal photon should have the same phase relationship to the stimulating tickler beam) but if so the problem is why which-path information can't be taken from the idler photon?

 

[cesiumfrog]

There is a paper on this topic ("Control of Young's fringes visibility by stimulated down-conversion", PRA v.51 p.1631 '95). They keep the pump beam on, and vary the intensity of the "inducing" beam (with no particular measurement made of the idler). The signal photons are directed to a screen via a double-slit. For low inducer intensity, the entangled pairs are produced spontaneously (with a superposition of random possible starting phase) giving no raw interference pattern. As intensity goes up, the entangled pair production tends to be stimulated (in phase with the inducing beam) and a raw interference pattern emerges smoothly.

Of course, that's useless for these purposes: when the inducing intensity is high enough that the signal photon develops coherent phase, it will undoubtedly also be impossible to distinguish which idler photon it is entangled with.

 

[bruce2g]

...
What I am saying is, that we have a superposition of all possible phases emitted and therefore also a superposition of all possible phase differences between A and B as we do not have which way information. The additional phase shift due to path length differences is fixed. So we have a superposition of all possible total phase differences at the detector D0. When it comes to detection, those states, for which the total phase difference satisfies the criteria for constructive interference will contribute most to the detected photons. Those, which match the criteria for destructive interference won't contribute at all. Of course there are lots of states in between.

Anyway we have the same superposition on the idler side. The relative path length difference is fixed here as well. +pi/2 or -pi/2 for D1 or D2. As said above, on each detector, those states will contribute most, which satisfy the criteria for constructive interference.

So you get distribution for detection probability against phase difference of the initial state for each of the three detectors. Multiplying them will give you the fringes or antifringes.

Cthugha, I want to say at the outset that I really appreciate your contribution to this thread. I wrote a post about a year ago attempting to 'demystify' this experiment, and while I saw that there was a correlation between the phase of the idler paths and the phase of the signal paths, I never could figure out how the darn correlation came about. In hindsight, I'm a little embarrassed that I didn't see that it was due the difference between the random down-conversion times of the two crystals, so thank you for your patience in bringing us all to this point.

I'd like to point out that this also means that the significance of the 'delayed choice' aspect of the experiment is perhaps somewhat overrated. Both the signal and idler photon measurements are observables related to the phase difference between the two paths, and it doesn't matter which one you measure first.

It is a cool experiment, however; I was especially intrigued by the fact that the crystals are themselves in a superposition of |left crystal emits entangled pair> + |right crystal emits entangled pain> and that the interference results from this superposition. I sure hope they can come up with another experiment in the future whose results are a little more surprising.

 

[bruce2g]

parting thought: walborn?

I wonder if the S.P. Walborn, M. O. Terra Cunha, S. Pádua and C. H. Monken, et al experiments described in http://grad.physics.sunysb.edu/~amarch/Walborn.pdf (and with a nice intro version at http://www.mat.ufmg.br/~tcunha/2003-07WalbornF.pdf ) would also have an explanation as simple as this one.

There, the spdc comes before the slits; signal photons are sent through the slits and then through quarter wave plates (one placed after each slit, to mark the which-path information); if you put a diagonal polarizer before the idler detector, you'll see interference in the coincidence counts; a horizontal or vertical polarizer on the idler gives a gaussian lump.

The Walborn et al version of the delayed choice eraser hasn't gotten much attention on this forum, probably because it doesn't have as many holes in it for us to poke at. Maybe someone has some insight they could share now, or else I think I'll try and grind through the math for a few weeks and maybe bring it up in a new thread.

 

[RandallB]

I'd like to point out that this also means that the significance of the 'delayed choice' aspect of the experiment is perhaps somewhat overrated. Both the signal and idler photon measurements are observables related to the phase difference between the two paths, and it doesn't matter which one you measure first.

It is a cool experiment, however; I was especially intrigued by the fact that the crystals are themselves in a superposition of |left crystal emits entangled pair> + |right crystal emits entangled pain> and that the interference results from this superposition. I sure hope they can come up with another experiment in the future whose results are a little more surprising.

the significance of this 'delayed choice' overrated !

crystals are themselves in a superposition ??
- - On what basis can you presume two separate physical crystals are in superposition?
You have two signal photons and two idler photons to solve this paradox based on phase differences and suddenly this 'delayed choice' paradox is no longer surprising and has no mystery left in it for you? Yes I’ll agree the solution you are describing is simple, you need to look to its originator to see how simple. You solution here is based on wave interference as put forward by John Young round about 1805!

You are missing the point of this experiment by assuming you have 4 photons.
Allowing two signal photons one from each slit and two idler photons one from each slit is simply not possible. The only way that happens is if you coordinate two photons to fly at the double slit together one for each of the two slits – that is not how this experiment is set up. They specifically insure that only one photon capable going through just one for the two slits is presented to the double slit at a time. Therefore there can only be one signal and one idler photon produced together from just one slit. There is no two signals to phase interfere with each other, nor two idlers to phase interfere with each other. Yet wave/phase patterns can be found as if beams of light full of photons were being used. This is not a Young test it is a Quantum test.

Walk through the experiment again using a single photon from the start passing one slit/crystal and you should see how you are underrating just how surprising this experiment still is.

 

[bruce2g]

the significance of this 'delayed choice' overrated !

crystals are themselves in a superposition ??
- - On what basis can you presume two separate physical crystals are in superposition?.

I know it sounds strange for two macroscopic crystals to be in a superposition. But, as I understand it, in SPDC there is one atom or molecule in the crystal which is brought to an excited state and which later emits the matched pair. So, until one of the paired photons is detected, it is not known which crystal contains the molecule which emits the entangled pair, and so maybe it's more comfortable to think that it's just a couple of molecules which are in superposition.

You have two signal photons and two idler photons to solve this paradox based on phase differences and suddenly this 'delayed choice' paradox is no longer surprising and has no mystery left in it for you? ...
You are missing the point of this experiment by assuming you have 4 photons.
Allowing two signal photons one from each slit and two idler photons one from each slit is simply not possible. Walk through the experiment again using a single photon from the start passing one slit/crystal and you should see how you are underrating just how surprising this experiment still is.

I only have one signal and one idler at a time, but since the pump photon is in the superposition 1/sqrt(2)(|goes through left slit>+|goes through right slit>), the signal and idler each have two possible points of origin.

The SPDC crystals also introduce a random phase difference between the left and right paths. So, even though only one idler is actually created (in this universe, at least ;-), both idler paths must be possible in order for this phase difference to have an effect (it determines the probability that the idler will be detected at D1 vs D2). Similarly for the signal photon: both paths must be possible all the way to the detector in order for the phase difference to have an effect, and this also requires that the crystals be in a state of superposition (well, we know there's one excited molecule, but we don't know which crystal it is in).

So even though there are just two photons, there must be four possible paths.

Thanks for posing the question. At a deeper level, I think we should probably say 'the system behaves as if the crystals were in superposition,' since I think that's more accurate.

 

[RandallB]

But, as I understand it, in SPDC there is one atom or molecule in the crystal which is brought to an excited state and which later emits the matched pair. So, until one of the paired photons is detected, it is not known which crystal contains the molecule which emits the entangled pair, and so maybe it's more comfortable to think that it's just a couple of molecules which are in superposition.

That doesn't work since all Delayed Choce experiment require thosands of samples - - do all thos tests hit the same two molecules that are in entanglement - QM simply does not require this period.

You "can think of it as if it were so", but that is not helpful to science

So even though there are just two photons, there must be four possible paths.

Thanks for posing the question. At a deeper level, I think we should probably say 'the system behaves as if the crystals were in superposition,' since I think that's more accurate.

No it is not at a deeper level your taking it to a superficial level where you say even though there are only two photons we can imagine there are four and solve the problem as easily as Young did over a century ago. Then you get to walk away from the problem thinking you’ve “solved another one” when a real scientific problem that deserves to have a real answer some day is trivialized.

The same approach will solve the “Walborn et al version of the delayed choice eraser” just as well. But again, it does not help advance science.
I’d rather know I still had a problem the remained unexplained, then pretend I’d figured it out so I could put it out of mind. Not a posing a question, just sharing an opinion.

 

[cesiumfrog]

That doesn't work since all Delayed Choce experiment require thosands of samples - - do all thos tests hit the same two molecules that are in entanglement - QM simply does not require this period.

Would you clarify this?

Are you agreeing with bruce, when you mention "two molecules", in that there must initially be multiple (separated) possible origins for each signal photon (similarly to how Young's interference requires illumination from two slits)?

Or are you saying something else (in which case, could you specify precisely what part of the experiment is not required, and what evidence there is for that statement)?

The same approach will [correctly predict results for various experiments]. But again, it does not help advance science. [..] Not a posing a question, just sharing an opinion.

You're saying that you feel you need a "deeper" (more classically intuitive) explanation for the results of quantum mechanics? Is this related to your personal (non-mainstream) preference for a hidden variable theory of QM?

 

[bruce2g]

... No it is not at a deeper level your taking it to a superficial level where you say even though there are only two photons we can imagine there are four and solve the problem as easily as Young did over a century ago. ...

I know it seems strange that you can superimpose the two paths, especially when something as complicated as SPDC needs to "happen" at both crystals. But analyzing the problem in this manner works out the correct answer mathematically when, as Feynman put it, you "sum over all the histories." It is really amazing that this works! I can't really imagine how all these complex histories (e.g., a separate SPDC in front of each slit) can be summed together if only one "really" happens (only one photon pair is "really" produced).

Maybe some other mechanism introduces the phase difference between the two paths. Or, maybe the idler's probability of choosing D1 over D2 is based on something else besides a phase difference between the two paths. I keep trying to figure out some more intuitive explanation myself, but I haven't had much luck so far, but maybe you will!

 

[RandallB]

Are you agreeing with bruce, when you mention "two molecules",

You're saying that you feel you need a "deeper" (more classically intuitive) explanation for the results of quantum mechanics? Is this related to your personal (non-mainstream) preference for a hidden variable theory of QM?

Not at all, just That Bruce is depending on "something" going through 2 signal paths and 2 idler paths that is total inconstant with QM. At least Copenhagen oQM with HUP. Sure he can explain it with a BM like wave action of hidden guide waves, others can use MWI, or even Strings. The experiment is not confirming anyone of these theries a correct is it?

But Bruce seemed to think that this was so easy to completely solve he was hoping for something a bit more challenging. Well if anyone needs something challenging to work on how about explaining the how the HUP, (or superposition or whatever) measures where the second slit is and works with the real photon that does go through.

That should be surprising enough if able to be explained at all. He just seemed bored by the experiment at the end of Post #33 -- and IMO that experiment is no less surprising Walborn or any other delayed choice experiment – that’s all

 

[Hurkyl]

I keep trying to figure out some more intuitive explanation myself, but I haven't had much luck so far, but maybe you will!

Sometimes, the best way to find an intuitive explanation of something is to study it until it becomes intuitive. Then, it is its own intuitive explanation.

 

[bruce2g]

But Bruce seemed to think that this was so easy to completely solve he was hoping for something a bit more challenging. ... He just seemed bored by the experiment at the end of Post #33

I was noting that the authors claim that the SPDC's destroy the interference by providing which-path information, and then restore it by erasing the which-path information at the final idler beam splitter. There is a 'delayed choice' since the final idler beam splitter occurs after the signal photons have been detected.

In this thread, we've discovered that the SPDC's destroy the interference by inducing a random phase difference between the two paths; the signal photon's X position and the idler's probability of going to D1 or D2 both derive from that phase difference, and this creates fringes in coincidence with D1 and anti-fringes with D2. In this view, there is no "delayed choice," and so that's why I think that part is overstated.

 

[cesiumfrog]

I was noting that the authors claim that the SPDC's destroy the interference by providing which-path information, and then restore it by erasing the which-path information at the final idler beam splitter. There is a 'delayed choice' since the final idler beam splitter occurs after the signal photons have been detected.

In this thread, we've discovered that the SPDC's destroy the interference by inducing a random phase difference between the two paths; the signal photon's X position and the idler's probability of going to D1 or D2 both derive from that phase difference, and this creates fringes in coincidence with D1 and anti-fringes with D2. In this view, there is no "delayed choice," and so that's why I think that part is overstated.

I think that's a misunderstanding.

In the classic DCQE, the "choice" is not at the final beam splitter (D1 vs D2), but at the pair of preceding beam splitters (D1-2 vs D3-4) which could in principle be removed and optionally replaced (even at the last moment) by a pair of mirrors. This option would facilitate one to choose whether to measure which-path information or to measure phase-difference information, and this choice is "delayed" in the sense that in principle the experimenter can make the decision after detecting the signal particle's position.

I'd also be careful how much weight you give to the uncovery (is that a word?) of an attributable mechanism for the path phase differences (ie. spontaneous-PDC). It is a general result from the QM theory that the which-path measurement erases phase-difference information, and vice-versa... basically it's the uncertainty principle, not just some artefact of their one particular experimental apparatus. Attempting to produce this experiment's entangled particles by some "better" method (plus the related analysis) would be interesting, but one would expect equivalent results (eg. raw signal pattern independent of measurement choice).

 

[ganstaman]

Hello all, hope this is an ok first post. Going back to the Kim/Scully experiment for a moment:

First, thanks to everyone so far who made it make more sense than it ever did before.

Second, can this modification/jumbled-late-night-idea be explained (I don't think it's been asked yet, but after reading through all this, it's very possible I simply forgot). Ok, so all the photons have hit the screen. As it is (in figure 1 of the pdf posted on page 1 here), the subset of photons entangled with idler photons detected at D3 form no interference pattern. Same for D4. But the subset of photons entangled with idler photons detected at D1 (or D2) will show an interference pattern. This pattern, though, is 'hidden' in the non-interference pattern on D0.

However, after all the photons hit the screen, you could have modified the back end. You could have made it so that photons heading towards D4 or D3 would instead be routed towards the D1/D2 combo, and photons heading towards D1/D2 would instead head to D4 and D3 (obtaining the which path info). Unless QM is more messed up than I thought, this will cause a different subset of photons to be at D1 than before. And yet, I still expect the subset related to D1 to show the IP. This implies to me that there are many possible IPs available yet 'hidden' in the non-IP we see on the screen (it may be mathematically intuitive that the many IPs exist, but that they do coincide with the D1/D2/D3/D4 set-up requires the weirdness of QM).

So, what I'd really like to do is make it more of a conscious choice. We will remove BSA and BSB and instead simply place a switch or something there so that we can choose to send the photon to D4 or D3, or to D1/D2. After each photon hits the screen, we can then decide whether we'd like which-path-info (send it to D4 or D3 -- not our choice, but we open it up so that depending on which side it's on, it will go to one of those) or not (send it to D1/D2). Even though we made this choice, I think we should see no IP with the subset from D3 or D4, but we should from the subsets of D1 or of D2.

However, we could have chosen any of the possible combination of choices (for each photon we had 2 choices) and for each combination, it just works out that the IP is formed for the right subset. Does this make any sense? Does it have any relevance, or has been tested?

 

[bruce2g]

So, what I'd really like to do is make it more of a conscious choice. We will remove BSA and BSB and instead simply place a switch or something there so that we can choose to send the photon to D4 or D3, or to D1/D2. After each photon hits the screen, we can then decide whether we'd like which-path-info (send it to D4 or D3 -- not our choice, but we open it up so that depending on which side it's on, it will go to one of those) or not (send it to D1/D2). Even though we made this choice, I think we should see no IP with the subset from D3 or D4, but we should from the subsets of D1 or of D2.

I'm sure that you are right.

You can look at http://arxiv.org/pdf/quant-ph/0610241 which shows that for the 'delayed choice' part, you can switch the photons at the last instant between 'which path' and 'erasure', and you get interference on the photons which go to the beam splitter and you don't get interference on the photons which provide which-path information. Their setup is a little different, but the principle is the same.

Wheeler's interpretation is that somehow the photon just goes through one slit if it's going to be detected, and it goes through both slits otherwise. No one has been able to prove that this interpretation is correct, but no one has been able to disprove it either. It sounds a little strange, because the decision to measure the path is done randomly after the photon has gone through the slit, so the photon needs to somehow communicate with the future state of the detector when it takes its path(s) through the slits. On the other hand, the other explanations (collapse of the wave function, multiple worlds, etc.) are also kind of hard to swallow, so the jury is still out.

 

[bruce2g]

I think that's a misunderstanding.

In the classic DCQE, the "choice" is not at the final beam splitter (D1 vs D2), but at the pair of preceding beam splitters (D1-2 vs D3-4) which could in principle be removed and optionally replaced (even at the last moment) by a pair of mirrors. This option would facilitate one to choose whether to measure which-path information or to measure phase-difference information, and this choice is "delayed" in the sense that in principle the experimenter can make the decision after detecting the signal particle's position.

What I was saying was that you can start your explanation at D0; after the signal photon has been detected there, you can choose whether to send the idler to the interfererometer at D1/D2, which will show interference based on the phase revealed by D0, or you can send the idler to D3/D4, which will not show any relationship to the phase revealed by D0. This explanation is consistent with the observed results (and far more intuitive), and does not involve any 'delayed choice'.

I have noticed that when you deal with entangled photons, it never matters which one you detect first. You always get the same results no matter which one you measure first. (I believe this is due to the fact that in different relativistic frames, either measurement could be seen as 'first' if the measurements are space-like separated.) So, I prefer the explanation in which D0 is measured first and the other measurements follow in a consistent manner, because in fact, D0 is measured first and the other measurements follow!

 

[cesiumfrog]

What I was saying was that [..] after the signal photon has been detected there, you can choose [..]

I agree: we can make a choice, and as you said, our choosing may also be postponed until after the signal photon has been detected (note the separation could be time-like, in which case all observers agree on the ordering). Let's both call it "choosing after".

does not involve any 'delayed choice'.

Not sure what you're getting at there.

One might better accept the title of the paper in terms of historical context. The original excitement about this specific experiment was presumably that nobody before had shown the "choosing" could be done "after" detecting the signal photon (and many back then might have expected different results... we of course have the benefit of hindsight in our own interpretations). Hence delayed choice is core to the paper, though now I would criticize the "eraser" part (since information is not destroyed but just recorded in a different basis, and this is a common source of misinterpretation, but again historically they were only following on from the terminology of previous work in their field).

 

[peter0302]

Ok I read this whole thread (painful) and I might have missed it, but has anyone explained WHY the two erase paths, D1 and D2, cannot be brought back into phase, through additional beam splitters, so that we can observe an interference pattern at D0 without the need to distinguish between detections from D1 and D2?

 

[StevieTNZ]

Even in the case of the normal delayed choice quantum eraser setup where the which-path information is erased, the total pattern of photons on the screen does not show any interference, it's only when you look at the subset of signal photons matched with idler photons that ended up in a particular detector that you see an interference pattern. For reference, look at the diagram of the setup in fig. 1 of this paper:

http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9903/9903047.pdf

In this figure, pairs of entangled photons are emitted by one of two atoms at different positions, A and B. The signal photons move to the right on the diagram, and are detected at D0--you can think of the two atoms as corresponding to the two slits in the double-slit experiment, while D0 corresponds to the screen. Meanwhile, the idler photons move to the left on the diagram. If the idler is detected at D3, then you know that it came from atom A, and thus that the signal photon came from there also; so when you look at the subset of trials where the idler was detected at D3, you will not see any interference in the distribution of positions where the signal photon was detected at D0, just as you see no interference on the screen in the double-slit experiment when you measure which slit the particle went through. Likewise, if the idler is detected at D4, then you know both it and the signal photon came from atom B, and you won't see any interference in the signal photon's distribution. But if the idler is detected at either D1 or D2, then this is equally consistent with a path where it came from atom A and was reflected by the beam-splitter BSA or a path where it came from atom B and was reflected from beam-splitter BSB, thus you have no information about which atom the signal photon came from and will get interference in the signal photon's distribution, just like in the double-slit experiment when you don't measure which slit the particle came through. Note that if you removed the beam-splitters BSA and BSB you could guarantee that the idler would be detected at D3 or D4 and thus that the path of the signal photon would be known; likewise, if you replaced the beam-splitters BSA and BSB with mirrors, then you could guarantee that the idler would be detected at D1 or D2 and thus that the path of the signal photon would be unknown. By making the distances large enough you could even choose whether to make sure the idlers go to D3&D4 or to go to D1&D2 after you have already observed the position that the signal photon was detected, so in this sense you have the choice whether or not to retroactively "erase" your opportunity to know which atom the signal photon came from, after the signal photon's position has already been detected.

This confused me for a while since it seemed like this would imply your later choice determines whether or not you observe interference in the signal photons earlier, until I got into a discussion about it online and someone showed me the "trick". In the same paper, look at the graphs in Fig. 3 and Fig. 4, Fig. 3 showing the interference pattern in the signal photons in the subset of cases where the idler was detected at D1, and Fig. 4 showing the interference pattern in the signal photons in the subset of cases where the idler was detected at D2 (the two cases where the idler's 'which-path' information is lost). They do both show interference, but if you line the graphs up you see that the peaks of one interference pattern line up with the troughs of the other--so the "trick" here is that if you add the two patterns together, you get a non-interference pattern just like if the idlers had ended up at D3 or D4. This means that even if you did replace the beam-splitters BSA and BSB with mirrors, guaranteeing that the idlers would always be detected at D1 or D2 and that their which-path information would always be erased, you still wouldn't see any interference in the total pattern of the signal photons; only after the idlers have been detected at D1 or D2, and you look at the subset of signal photons whose corresponding idlers were detected at one or the other, do you see any kind of interference.

Saw this post earlier, and I've been racking my brain over Quantum Erasering today.
If I understand correctly, if you view the signal photons you see an interference pattern, and if you view only the idler photons, you see an interference pattern, but combing the two cancels each other out (much like in the 4 --> in the pdf attached)?

So really the original interference pattern is NOT recovered through information erasing, instead two new interference patterns are displayed?

 

[JesseM]

If I understand correctly, if you view the signal photons you see an interference pattern, and if you view only the idler photons, you see an interference pattern, but combing the two cancels each other out (much like in the 4 --> in the pdf attached)?

No, the idlers are only detected at 4 possible locations so they don't form any sort of continuous pattern, while the signal photons are detected at a range of locations but the total pattern of signal photons is always a non-interference pattern. The idea is that if you look at the subset of signal photons whose corresponding idlers went to D1, you do see interference in that subset; likewise if you look at the subset of signal photons whose corresponding idlers went to D2, you also see interference in that subset. But the peaks of one interference pattern line up with the valleys of the other and vice versa, so their sum--which would be the total collection of signal photons if you replaced beam-splitters BSA and BSB with mirrors (so all idlers went to either D1 or D2, rather than some going to D3 or D4 as in the normal setup)--is a non-interference pattern.

The link in the post of mine you quoted isn't working any more, but here's a version of the paper that works, if you take a look at Fig. 1 from P. 4 (as well as Fig. 3 and Fig. 4 showing the pattern of the subsets of signal photons whose idlers went to D1 and D2 respectively) my explanation in the original post should be easier to follow:

http://arxiv.org/pdf/quant-ph/9903047v1

 

[StevieTNZ]

Sorry if this sounds stupid, but what exactly are idler photons? I'm reading this book that mentions the University of Rochester experiment by Mander that contains signal photons and idler photons. So we have a laser and a beam splitter, each path contains either the signal photons or the idler photons?

So when you say the subset of signal photons and their corresponding idler photons, what do you mean? Is that some of the signal photons that went on one path at the first beam splitter and some of the idler photons that went on the other path at the beam splitter?

Not too sure. Sorry if it sounds silly. Hopefully I'll realize what is being said once I'm given some clarification!

But either way, the original interference pattern is NOT recovered, but two new interference patterns are created which cancel each other out?

 

[JesseM]

Sorry if this sounds stupid, but what exactly are idler photons?

"signal" vs. "idler" are just two labels to distinguish members of an entangled pair of photons, they don't imply any intrinsic difference between the two photons, the "idlers" are just the ones that go in the direction of the D1/D2/D3/D4 detectors in the diagram while the "signal" photons are the ones that go in the direction of the D0 detector in the diagram.

So when you say the subset of signal photons and their corresponding idler photons, what do you mean? Is that some of the signal photons that went on one path at the first beam splitter and some of the idler photons that went on the other path at the beam splitter?

Each photon is created as part of an entangled pair, so each signal photon has an entangled idler "twin". So if you have 1000 signal photons recorded at D0, you can label each one according to where their idler "twin" was detected, at D1 or D2 or D3 or D4. Suppose there are 250 signal photons whose idler twins went to D1, if you graph only that subset of signal photons (i.e. not including the positions of any of the other 750 signal photons on your graph) then you will see an interference pattern. Likewise if there are 250 signal photons whose idler twins went to D2, if you graph that subset you also see an interference pattern, but displaced from the first one so that the peaks of the second interference pattern line up with the valleys of the first and vice versa. Because of this displacement, if you graph the 500 signal photons whose idler twins went to either D1 or D2, you see a non-interference pattern. And since the D3/D4 subsets also are non-interference patterns, if you graph the total pattern of all 1000 signal photons, you get a non-interference pattern.

But either way, the original interference pattern is NOT recovered, but two new interference patterns are created which cancel each other out?

By "original" do you mean what would be seen in a regular double-slit experiment with non-entangled photons? If so, assuming what you mean here matches what I said above (that the total pattern of all 1000 signal photons shows no interference, but if you graph the 250 whose idlers went to D1 or the 250 whose idlers went to D2, you do get two interference patterns which add up to a non-interference pattern when you combine their data) then yes.