How and what mechanism does govern the failure of visible interference pattern and formation of analytical interference pattern in DCQE experiment?

Question

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Preface: This is a follow-up question to the following two questions:

1. Does simply putting a photon-splitting crystal after a double slit break the interference pattern?

2. Simplified delayed choice quantum erazer experiment: is it possible to create an interference pattern at D0?

And also relates to this question: Interference pattern in delayed choice quantum eraser (Answers to which are not satisfactory to me and anyways my question encompasses whole phenomena not a part of it)

I found several other Questions that touch on related aspects but are not quite the same and answers seem to circumvent the facts that I want to be revealed in answers to this question.

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Background:

The foundations of quantum mechanics are plagued by conceptual paradoxes that challenge our intuition of reality. For example, in 1926 Gilbert N. Lewis proposed a delayed-choice thought experiment which appeared to show retrocausation in the Conventional Formulation of quantum mechanics. Retrocausation, also known as future input dependence, is when a model parameter associated with time t depends on model inputs associated with times greater than t. He considered a double-slit interference experiment using a single photon from a distant star. A millennia after the photon has left the star, but just before it reaches the two slits (A and B) on Earth, we randomly choose to either keep both slits A and B open, or intervene to close slit A only, or intervene to close slit B only. Repeating this experiment for a large number of single photons, an ensemble of experimental results can be obtained. Weizsäcker and Wheeler later rediscovered and elaborated on Lewis’s thought experiment.

A related

delayed-choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, and reported in early 1998, is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald Wheeler's delayed-choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

--- https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser

Experimental setup Kim et al

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Analytical (coincidence results between $D_0$ and $D_1$, $D_2$, $D_3$, $D_4$) results. ($R_{04}$ is not provided in the Kim article and is supplied [as per in Wikipedia] according to their verbal description.)

The total pattern of all signal photons at $D_0$, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons. One can get an idea of how this works by looking at the graphs of $R_{01}$, $R_{02}$, $R_{03}$, and $R_{04}$, and observing that the peaks of $R_{01}$ line up with the troughs of $R_{02}$ (i.e. a π phase shift exists between the two interference fringes). $R_{03}$ shows a single maximum, and $R_{04}$, which is experimentally identical to $R_{03}$ will show equivalent results. The entangled photons, as filtered with the help of the coincidence counter, are simulated in Fig. 5 to give a visual impression of the evidence available from the experiment. In $D_0$, the sum of all the correlated counts will not show interference. If all the photons that arrive at $D_0$ were to be plotted on one graph, one would see only a bright central band.

-Wikipedia

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It was argued (I may add the phrase "quite misguided") that one possible way to understand the paradoxical results of a delayed choice experiment is to assume as previously mentioned that the future can affect the past (retro-causality). This means that the causal order of events is not fixed, but depends on quantum probabilities. This is an example of quantum causality, which differs from classical causality. However, there is a more reasonable (useful) interpretation of quantum mechanics that does not require retro-causality. It is called the realistic interpretation (REIN). According to this interpretation, the wave function is a real physical entity that describes the presence of a quantum object in disjointed regions of space. When a measurement is made, the wave function collapses instantaneously and the object is found to be located in one region only.

Additional:

1. An useful commentary on the experiment by Ross Rhodes: "A Delayed Choice Quantum Eraser" by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and Marlon O. Scully

2. An useful explanation: https://physics.stackexchange.com/a/18612/366787
   (Following is a direct link to the archived version of the author's own blog post for the complete explanation: Delayed choice quantum eraser) & a complete rejection of both the retrocausality and action at a distance by the same author (Luboš Motl): No retrocausality in QM, delayed choice quantum eraser . Also his primer on Quantum Entanglement: Entanglement at a distance

3. An useful research paper: Taming the Delayed Choice Quantum Eraser by Johannes Fankhauser- University of Oxford

4. An interesting view: Demystifying the Delayed Choice Experiments by Bram Gaasbeek- Institute for Theoretical Physics, Leuven, Belgium

5. A loophole: Current optical delayed-choice experiments, even those involving entangled light, can be understood from a strictly causal, classical perspective. : Classical model of delayed-choice quantum eraser by Brian R. La Cour∗ and Thomas W. Yudichak- Applied Research Laboratories, The University of Texas at Austin

6. Separation fallacy: Separation is where superposition collapses to eigenstates is a fallacy: A Common Fallacy in Quantum Mechanics: Why Delayed Choice Experiments do NOT imply Retrocausality by David Ellerman, University of California at Riverside (This is by far the most reasonable explanation why retrocausality is not needed for the validity of DCQE) (Also firmly in the framework of REIN [Realistic Interpretation] of Quantum Mechanics)

7. The long-held notion that in the delayed mode, the experimenter has a choice between reading the which-way information or erasing it, should be given up. In the delayed mode, the which-way information is always erased. : The Delayed-Choice Quantum Eraser Leaves No Choice by Tabish Qureshi- International Journal of Theoretical Physics & also related: Demystifying the Delayed-Choice Quantum Eraser by the same author

8. Inelastic scattering causes no interference: Which-way detector unlocks some mystery of the double-slit experiment- Phys.org

9. Einstein maintained that quantum metaphysics entails spooky actions at a distance; later experiments have shown that what bothered Einstein is not a debatable point but the observed behaviour of the real world.: Is the moon there when nobody looks? Reality and the quantum theory- by N. David Mermin, Horace White Professor of Physics Emeritus, Cornell University

10. For reference, the following research paper is a frail attempt at clutching the straws of retrocausality using a Time-Symmetric Formulation (TSF) of Quantum Mechanics (rejecting the arrow of time at the quantum scale): CAUSAL INTUITION AND DELAYED-CHOICE EXPERIMENTS by Michael B. Heaney

11. Extenstion to DCQE for disproving retrocausality: The Quantum Eraser Paradox by C. Bracken, J.R. Hance, and S. Hossenfelder

12. Estimated coincidence graphs in a more revealing experimental setup where the difference between $R_{03}$ and $R_{04}$ graphs is more visible:

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Main Question:

What is the exact mechanism or process that governs/causes the failure of the visible interference pattern and formation of the analytical interference pattern in the Delayed Choice Quantum Erasure (DCQE) experiment? (the version intended is Kim et al)

1. If we eliminate all the noise at SPDC (Spontaneous Parametric Down Conversion) stage, would an interference pattern become directly visible at any single detector ($D_0$, $D_1$, $D_2$, $D_3$, $D_4$) and why?

[My assessment is, if even we eliminate enough noise at SPDC and even background noise, a direct interference pattern at any detector should not be formed. (Not even a slight interference pattern)] [This is in contrast with this answer here ]

2. How exactly does an interference pattern form when you consider coincidences between $D_0$ and $D_1$ or $D_2$?

(Because how can energy deposits recorded at $D_0$ encodes an interference pattern to coincidence data between $D_0$ and $D_1$ or $D_2$ optically? That aspect is not clear at all.)

3. If there are no clear answers to the above, is the underlying mechanism not yet comprehended or discovered so only descriptions are possible (Or may it defy our conventional intuition or wisdom)?

4. If so, to what extent can you describe the mechanism at play determining the experiment results and how encoding interference pattern in coincidence results between $D_0$ and $D_1$ or $D_2$ happens?

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Why this is important: Because physics forums (including physics.stackexchange) are riddled with seemingly never-ending questions related to this experiment or similar setups including potential modifications that refers to a seeming retrocausal/ communication from future to past aspects of the experiment. While general consensus has been and should have been no retrocausality (which is however not universally accepted even among theoretical physicists and also causing the stirring of unwarranted discussion of other interpretations "such as many worlds intepretation" that are divergent from standard Copenhagen interpretation), all the explanations I have seen so far, including Youtube videos (eg. The Delayed Choice Quantum Eraser, Debunked) seems too cavalier towards the exact barebones mechanism that underlay this. They all seem to say "Oh, yeah. No - retrocausality because interference is already encoded in $D_0$ and nothing you do to other 'twin' affects 'primary signal twin' but in order to decode the pattern you need coincidence counter comparing between detections of $D_0$ and detections of receivers on the idler side. So whatever you do in future doesn't change the past, rather, what you do in future decides how the past is revealed to you", or hide under a nice & brief listing of quantum mechanical equations. While after carefully studying this and similar experiments, it should be obvious that no retrocausal effects are needed at all to explain the phenomena, these explanations however seem to skip the exact mechanism that governs the phenomena, so the typical layman has to accept or believe whatever they say at ad verbatim without intuition to the underlying process.

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Note: I do not want to restrict the freedom of answering this question but it will be helpful if:

• An answer address the whole issue that encompasses the question.
• Suitable for general audience.
• Clearly state (differentiate) whether the content of the answer is personal opinion or general consensus where suitable/applicable.
• Answer addresses issues standalone without the user having to refer to external sources ( However references to external sources to confirm the answer or parts of it are very much appreciated and encouraged).
• Visual representations if needed are appreciated.

I wanted to keep the question concise but also didn't want to leave ambiguousness as to what I meant, so it became quite a bit long. Apologies for that.

Side note: I know this is a pretty old experiment and a lot of perspectives and analyses may be circulating already. But I rather find it's a sea of misinformation, lots of incomplete explanations and misguided and unnecessary hype towards an unwarranted implication of retro-causality. Most of the explanations fail to provide a clear mechanism for how and why the experiment works the way it does. It seems to me that those types of explanations invite new complications than clarifying the already existing ones.

This question has been edited to suit later revealed facts to the OP and to make it clear to the reader, however, the main question and scope remain the same.

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Answer 1

First, just a general remark about interpretations. When we use the quantum mechanics formalism to compute predictions in experiments, such as the one here, it gives us the results that we can measure, but it does not give us the underlying mechanism. That is as far as the scientific method takes us. When we then try to understand why it works that way, we need do try and uncover the underlying mechanisms. For that we enter (a little bit) the domain of interpretations, which is going a little beyond the strict scientific method. We use such an interpretation to help us figure out what is going on.

Since we cannot use the scientific method to decide which interpretation is the correct one, we are free to pick any one. (All of them will give the same result. If this was not the case, we would have been able to use the scientific method to decide among them.) Then it makes sense to pick the simplest one. So, we can pick an interpretation which does not involve collapse (unless it would make some aspect clearer) and also does not involve branching into multiple universes. The simplest is one that just involves the unitary evolution of a superposition of different basis elements, which we can treat as different "realities." They are not realities in the sense we would normally think about them, because we can use a unitary transformation to redefine these realities in a different way.

Now to the experiment. (I want to redraw the setup in a simpler way, but have not had the time to do that yet. Perhaps I'll do that and add it here later.) What we have here is a scheme to perform the same experiment in different measurement bases. The four detectors, D1 to D4, all represent different measurement bases, two of them represent interferences between the two slits and two of them just measure the results from each of the slits separately. The different measurement bases are related by unitary transformations. Each measurement basis is a set of "realities" in superposition. So when a detection is registered in coincidence, it selects on specific "reality" from this set.

During the experiment, if we only look at what is detected at D0, we would see noise, which cannot be made any sense of. It would represent all the possible signals from all the possible measurement bases, together with those cases where the second photon was lost. The only way that we can extract sensible information from the measurements at D0 is when we only look at those measurements that are received at D0 in coincidence with measurements at a specific other detector. In that case, we restrict the measurements to a specific measurement basis, and all the accumulated measurements from the coincidences between those two detectors will give us the picture associated with that measurement basis only. That is why it is possible to obtain measurements from all four scenarios, simply by accumulating the statistics from the different coincidences.

For the delay aspect, we can now look at just one of these scenarios. Once the measurement basis is fixed, it does not matter which photon is measurement first. (However, some additional delay needs to be installed in how the coincidence is measured.) The results will be the same regardless of whether one photon is measure much later than the other.

In terms of causality, the whole state is produced in the nonlinear crystal. Everything that happens after that is just a matter of changing the measurement basis. In other words, everything that you observe regardless of which coincidence you look at or how much delay you introduce, it was caused by the state that was produced in the nonlinear crystal. So there is no violation of causality.

Hope this answer clarifies the confusion. If not, let me know.

Answer 2

You have asked for an account of what is happening in the DCQE experiment and have asked if eliminating noise at the SPDF would make fringes visible at a particular detector and how there can be fringes in the coincidence counts between different detectors.

The amount of noise in the SPDF doesn't explain the lack of fringes in the data on the results of measurements in each detector in isolation. It's a result of the fact that the photons are entangled in their position and so are unsharp in their position.

The DCQE experiment is pretty similar to the EPR experiment with some extra bells and whistles:

https://arxiv.org/abs/2210.11375

There has been a full account of what is happening in the EPR experiment for more than 20 years:

https://arxiv.org/abs/quant-ph/9906007

Information about the correlations is instantiated in the Heisenberg picture observables of the entangled systems, but the expectation value of those observables doesn't depend on that information - locally inaccessible information. This locally inaccessible information can only be recovered by interactions between systems containing that information. That information is usually carried in decoherent ("classical") channels but is protected from decoherence by its locally inaccessibility. That's why the fringes can only be see when the results of measurements are compared.

Answer 3

The short answer: If you consider virtual photons (forces) that are most likely present by excited electrons in a light source (BEFORE EMISSION) then it is possible to understand the famous statements by Dirac and Feynman ... "every photon interferes with itself" or stated in modern terms "every photon determines its own path". In order for "interference" to be observed we need the virtual/EM field to be affected by a double slit ...thus we would have to assume that the EM field is influenced by the the entire apparatus ... source, slits, crystal, polarizers.... detectors BEFORE photon emission ... the eventual photons just following most probable paths ... as described in the famous Feynman path integral.

What is also interesting is that photons also can take NON-"interfering" paths in this experiment ... the conclusion being the apparatus provided "probable" direct paths thru one slit to the detectors D3/D4.