The second sentence suggests that measuring the idler photon does not impact the signal pattern at all. — keystone

Yes.

The first sentence suggests that measuring the idler photon does give information on subsets of the signal pattern. — keystone

Yes.

If the second sentence were true, I would expect all 4 subsets to produce the same signal pattern. — keystone

Why would that be? Note, however, that the two phase subsets combined and the two path subsets combined do produce the same (non-interference) signal pattern.

IMHO, it seems like your mathematical explanation only supports your first sentence. How does it support your second sentence? — keystone

It doesn't. I'm assuming locality (and also no retro-causality) - here's an argument for it in a recent thread.

If the second sentence were true, I would expect all 4 subsets to produce the same signal pattern.
— keystone

Why would that be? — Andrew M

I'm wondering if my position could be made more clear if we focused on a simpler experiment. Let's assume that I've set up an experiment that starts similar to the DCQE. The entangled signal photons hit d0 and the idler photons have not yet hit PS. At this moment, does the signal pattern show interference? I don't think you can answer the question because you need to know what happens after this moment - you have to know what happens in the future. If after this moment, the idler photons travel through a lens and then hit a detector (akin to what happens to the signal photons), their path is unknown and I would expect to see an interference pattern for both the signal and idler photons. Or what happens to the signal pattern if the idler photons reflect off a mirror forever?

I'm assuming locality — Andrew M

My impression is that you may be holding a minority view here. Is that true? I think there is a subtlety related to quantum nonlocality in that it allows some information to be nonlocal but does not allow for faster-than-light communication. As for "The simple and obvious fact is that information has to be carried by material objects"...it's not that simple or obvious to me...even though it's obvious that Weinberg was a great man.

I'm wondering if my position could be made more clear if we focused on a simpler experiment. Let's assume that I've set up an experiment that starts similar to the DCQE. The entangled signal photons hit d0 and the idler photons have not yet hit PS. At this moment, does the signal pattern show interference? — keystone

No, the signal pattern never shows interference regardless of what happens to the idler photons. Interference is only revealed when the idler photons are detected at D1 and D2 and that information is later used to post-filter the signal pattern.

My impression is that you may be holding a minority view here. Is that true? — keystone

No, most physicists accept locality. See the Nielsen and Chuang quote here and the David Wallace quote here.

Quite a few interpretations, including Copenhagen and Many Worlds, have local dynamics. See the Local dynamics column in the quantum interpretations comparisons table.

I think there is a subtlety related to quantum nonlocality in that it allows some information to be nonlocal but does not allow for faster-than-light communication. — keystone

The latter is true for all interpretations. The former involves changes to the formalism (which Wallace refers to as "change the physics" strategies).

As for "The simple and obvious fact is that information has to be carried by material objects"...it's not that simple or obvious to me...even though it's obvious that Weinberg was a great man. — keystone

OK, though note that the quote was from physicist Asher Peres. (I think the Weinberg reference was just for the last sentence.)

No, the signal pattern never shows interference regardless of what happens to the idler photons. — Andrew M

Thank you for identifying the flaw in my example. I should have known that it wasn't so simple.

Interference is only revealed when the idler photons are detected at D1 and D2 and that information is later used to post-filter the signal pattern. — Andrew M

I'm still confused about how the interference pattern is entirely a postprocessing effect. It seems to me that the signal photons must "know" what will happen to the idler photons so that it can produce the correct signal during postprocessing. If the idler photons don't affect the signal photons, how is it that the "D1" signal photons produce a different signal than the "D2" signal photons?

No, most physicists accept locality. — Andrew M

Fair enough. I'll need to read those threads before bothering you with questions on locality.

See the Local dynamics column in the quantum interpretations comparisons table. — Andrew M

That's a great summary table. Thanks for sharing!

...and thanks for your continued comments. I feel like you're explaining things perfectly clear to me and I'm just not understanding!

I'm still confused about how the interference pattern is entirely a postprocessing effect. It seems to me that the signal photons must "know" what will happen to the idler photons so that it can produce the correct signal during postprocessing. If the idler photons don't affect the signal photons, how is it that the "D1" signal photons produce a different signal than the "D2" signal photons? — keystone

It follows from their joint entangled (Bell) state. Which, written in the z-basis (ignoring square root of two factors), is:

$|00\rangle + |11\rangle$

That state, written in the x-basis [*], where

$|0\rangle = \frac{|+\rangle + |-\rangle}{\sqrt 2}$ and $|1\rangle = \frac{|+\rangle - |-\rangle}{\sqrt 2}$ and, for reference, $|+\rangle = \frac{|1\rangle + |0\rangle}{\sqrt 2}$ and $|-\rangle = \frac{|1\rangle - |0\rangle}{\sqrt 2}$

is:

$|++\rangle + |--\rangle$

While it's true that the "D1" and "D2" signal patterns are hidden until post-processing, they are implicit in the D0 signal pattern regardless of what happens to the idler photons. This can be demonstrated by diverting the signal photons from D0 and instead sending them through a beam splitter to two new detectors D0a and D0b which will detect signal photons with states $|+\rangle$ and $|-\rangle$ respectively. The difference between those two states is a relative phase shift of -1 (or pi radians), which is what explains the slightly shifted interference patterns in the original experiment (i.e., R01 and R02).

Thus the signal photon's x-basis state will be directly observable as a detection event at D0a or D0b and predict which of detectors D1 or D2 the partner idler photon will later strike. Alternatively, if the idler beam splitters and detectors are removed altogether, that won't affect what is observed at D0a and D0b.

...and thanks for your continued comments. I feel like you're explaining things perfectly clear to me and I'm just not understanding! — keystone

You're welcome! If any of the above is not clear, I can break it down further.

--

[*] Most of the derivation is here, it can be completed by substituting the $|+\rangle$ and $|-\rangle$ identities from above.

This is all physics and a discussion between two people. It's admirable, but why not on the lounge?

This is all physics and a discussion between two people. It's admirable, but why not on the lounge? — jgill

It's about the delayed choice quantum eraser and the philosophical or foundational implications - a discussion which may sometimes require recourse to the physics of the experiment. From Wikipedia:

The delayed-choice quantum eraser experiment investigates a paradox. If a photon manifests itself as though it had come by a single path to the detector, then "common sense" (which Wheeler and others challenge) says that it must have entered the double-slit device as a particle. If a photon manifests itself as though it had come by two indistinguishable paths, then it must have entered the double-slit device as a wave. If the experimental apparatus is changed while the photon is in mid‑flight, then the photon should reverse its original "decision" as to whether to be a wave or a particle. Wheeler pointed out that when these assumptions are applied to a device of interstellar dimensions, a last-minute decision made on Earth on how to observe a photon could alter a decision made millions or even billions of years ago. — Delayed-choice quantum eraser - Wikipedia

For sure I would encourage people to join the discussion. For an accessible introduction, here's an excellent analysis and video of the experiment by physicist Sabine Hossenfelder.

I find this quote from wiki to be interesting:

In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects.

Thus the signal photon's x-basis state will be directly observable as a detection event at D0a or D0b and predict which of detectors D1 or D2 the partner idler photon will later strike. — Andrew M

Very interesting. I had assumed that beam splitters act entirely randomly, but from your description it seems that they do not. Is that correct? I think I'm slowly getting your point. At the act of entanglement the photons 'decide' how they're going to act, not just in measuring spin, but also in how they will behave at beam splitters and the phase of their interference pattern.

Let me ask you this then: you've mentioned the z-basis and the x-basis. Are there a finite number of bases or is the number infinite? I ask because if there are infinite, that seems like a lot of 'decisions' to make up front.

For an accessible introduction, here's an excellent analysis and video of the experiment by physicist Sabine Hossenfelder. — Andrew M

I actually find your latest example with D0a and D0b more convincing than Sabine's video.

Thanks!

At the act of entanglement the photons 'decide' how they're going to act — keystone

No wait…the first entangled photon’s behaviour is random but once measured, the other photons behaviour is determined? So in the DCQE are you saying that once the phase of the signals interference pattern is selected the fate of the idler photon is determined?

I find this quote from wiki to be interesting:

"In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects." — jgill

Yes, see the no-communication theorem.

The version of the no-communication theorem discussed in this article assumes that the quantum system shared by Alice and Bob is a composite system, i.e. that its underlying Hilbert space is a tensor product whose first factor describes the part of the system that Alice can interact with and whose second factor describes the part of the system that Bob can interact with. In quantum field theory, this assumption can be replaced by the assumption that Alice and Bob are spacelike separated.[9] This alternate version of the no-communication theorem shows that faster-than-light communication cannot be achieved using processes which obey the rules of quantum field theory. — No-communication theorem - Wikipedia

Very interesting. I had assumed that beam splitters act entirely randomly, but from your description it seems that they do not. Is that correct? — keystone

Yes, that's correct. It's only measurement that is (sometimes) random. To see this, take a look at this quantum coin example. In terms of a quantum coin, a beam splitter takes a coin in an initial state of $|heads\rangle$ and transforms its state to $|heads\rangle + |tails\rangle$. If the coin is measured, the result is random. If the coin is not measured, but sent through another beam splitter, then the beam splitter transforms its state from $|heads\rangle + |tails\rangle$ to $|heads\rangle$. If the coin is then measured, the result is $|heads\rangle$ with certainty. Similarly, with two beam splitters in series, $|tails\rangle$ goes to $|heads\rangle - |tails\rangle$ and then goes to $|tails\rangle$.

I think I'm slowly getting your point. At the act of entanglement the photons 'decide' how they're going to act, not just in measuring spin, but also in how they will behave at beam splitters and the phase of their interference pattern. — keystone

That would be one possible interpretation. Bohmian Mechanics acts non-locally. Many Worlds takes all possible paths. Copenhagen is silent on what happens.

Let me ask you this then: you've mentioned the z-basis and the x-basis. Are there a finite number of bases or is the number infinite? I ask because if there are infinite, that seems like a lot of 'decisions' to make up front. — keystone

Either infinite, or a very large finite number. And, yes it does. Also, Bell's Theorem places strong constraints on how that could work.

At the act of entanglement the photons 'decide' how they're going to act
— keystone

No wait…the first entangled photon’s behaviour is random but once measured, the other photons behaviour is determined? So in the DCQE are you saying that once the phase of the signals interference pattern is selected the fate of the idler photon is determined? — keystone

Yes, in the sense that the open possibilities for the idler photon have been reduced. The issue itself reduces to the EPR paradox. If the entangled state of the system is $|01\rangle - |10\rangle$, and Alice measures $|0\rangle$ (thus collapsing the state of the system to $|01\rangle$), she knows that when she meets up with Bob, he will have measured $|1\rangle$. For the above singlet state, that's true in any basis, assuming Alice and Bob measure in the same basis.

Thanks @Andrew M! You’ve cleared up much of my confusion. I understand that a lot of the mystery of the DCQE experiment can be addressed by fully appreciating what happens at entanglement. Delayed choice is actually a bit of a misnomer. I’ll need to let this continue to sink in further but I’d say you’ve addressed my initial question so thanks. Case closed!

I’ll need to let this continue to sink in further but I’d say you’ve addressed my initial question so thanks. Case closed! — keystone

:up:

Thanks for a great discussion!