# What happens to Entangled Photons after a polarizing beamsplitter (PBS)?

Gold Member

## Main Question or Discussion Point

SpectraCat and I have been discussing what happens to entangled photons after encountering a polarizing beamsplitter (PBS). A beer rides on the outcome (in addition to one I already won), so you know I can't let this go.

SpectraCats says: collapse of the wave function occurs at the PBS.
I say: the photon must be detected after the PBS for collapse to occur.

Now, the relevant issue is whether in a delayed choice experiment, the collapse occurred before or after some event (it doesn't matter for the discussion what event). The key is that in the experiment, which is referenced below, collapse should be measured relative to the PBS or the detectors.

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

Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping
Authors: Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, Anton Zeilinger

My argument is simple: it is the final context of the entire experiment that matters. After encountering a PBS, the outputs can - in principle - be reassembled and thus the "measurement" would be erased. SpectraCat disagrees with this, at least in the situation where no erasure occurs.

I am starting a new thread so we can discuss the issue of collapse - and how to probe it - assuming that collapse is a physical event. Your thoughts are welcome on the above question.

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Demystifier
Gold Member
SpectraCats says: collapse of the wave function occurs at the PBS.
I say: the photon must be detected after the PBS for collapse to occur.
I agree with you.

Now, the relevant issue is whether in a delayed choice experiment, the collapse occurred before or after some event (it doesn't matter for the discussion what event).
After. The (effective) collapse occurs when the coherent wave interacts with the measuring apparatus or any other environment with a large number of uncontrollable degrees of freedom, which causes irreversible decoherence.

My argument is simple: it is the final context of the entire experiment that matters.
My argument is even simpler. A true collapse never occurs. It is decoherence caused by interaction with other uncontrollable degrees of freedom that creates the illusion of collapse.

Gold Member
I agree with you.
Woo-hoo! I think I am half way to that beer now.

SpectraCat
Woo-hoo! I think I am half way to that beer now.
Not so fast ... first of all, the first beer you say you "won already" actually rides on the outcome of this second result, because if your interpretation is incorrect here, then you will not have shown experimental verification for your original statement that I took issue with.

Now for a correction, your statement
SpectraCats says: collapse of the wave function occurs at the PBS.
Is in fact not what I said ... since you are such a fan of context, you should not take my comments out of same.

My complete argument is that the detection (or decoherence) of the "non-interacting photons" (A and D in you example) must occur after the other photons (B & C), interact at the PBS, in order for the entanglement to be observed. This statement is in fact consistent with all the experiments that I have been able to find in the literature. The reason I believe the above statement is correct is that, if the detection of the A & D photons occurs before the B and C photons interact at the PBS, then there is no entanglement left to be teleported, because the initial entangled states (A with B and C with D) have been destroyed by the measurement, so the states of B and C are completely resolved when they enter the beam splitter.

Now that I have clarified my position on this, I think that Demystifier's post does not really resolve anything, and may in fact actually support my argument.

his statement,

After. The (effective) collapse occurs when the coherent wave interacts with the measuring apparatus or any other environment with a large number of uncontrollable degrees of freedom, which causes irreversible decoherence.
suggests that the real question we should be considering is whether or not the interaction of the B and C photons at the PBS constitutes an interaction "with the measuring apparatus or any other environment with a large number of uncontrollable degrees of freedom".

I tend to think the answer is "yes it does". So that would indicate that the interaction at the PBS is FAPP irreversible, which supports my claim.

Gold Member
1. Is in fact not what I said ... since you are such a fan of context, you should not take my comments out of same.

2. My complete argument is that the detection (or decoherence) of the "non-interacting photons" (A and D in you example) must occur after the other photons (B & C), interact at the PBS, in order for the entanglement to be observed. This statement is in fact consistent with all the experiments that I have been able to find in the literature. The reason I believe the above statement is correct is that, if the detection of the A & D photons occurs before the B and C photons interact at the PBS, then there is no entanglement left to be teleported, because the initial entangled states (A with B and C with D) have been destroyed by the measurement, so the states of B and C are completely resolved when they enter the beam splitter.
1.

2. You can measure A & D first, no question there I am sure you agree. The question then becomes, what are you doing when you measure B & C later in the PBS+detectors. The answer is, you are throwing A & D into one of several possible entangled states. You don't know which one yet. We should agree on this too.

Our point of departure is that you say the B & C PBS must come after the A & D detections for there to be Delayed Choice. I say only the *detections* for B & C must occur after the A & D detections for there to be Delayed Choice. My position is consistent with the source reference.

If there is collapse at the PBS, is there anyway to physically test that or otherwise probe it? Certainly, collapse occurs by the point of detection (we should agree on that even if you think it already happened earlier). I suggested previously that no experiment can settle this question, and am wondering if there are techniques that could expose more.

If your position were correct, might there be a different result if the PBS were changed in its position (i.e. later) ? I don't expect that would happen.

If hermitian operators $$H_A$$ and $$H_B$$ commute,
then
$$e^{-iH_A\tau_A/\hbar}e^{-iH_B\tau_B/\hbar}=e^{-iH_B\tau_B/\hbar}e^{-iH_A\tau_A/\hbar}$$.

Operators on different subsystems always commute.
Therefore it doesn't matter whether you interact with photons 1&2 first or photons 3&4.

SpectraCat
1.

2. You can measure A & D first, no question there I am sure you agree. The question then becomes, what are you doing when you measure B & C later in the PBS+detectors. The answer is, you are throwing A & D into one of several possible entangled states. You don't know which one yet. We should agree on this too.

Our point of departure is that you say the B & C PBS must come after the A & D detections for there to be Delayed Choice. I say only the *detections* for B & C must occur after the A & D detections for there to be Delayed Choice. My position is consistent with the source reference.

If there is collapse at the PBS, is there anyway to physically test that or otherwise probe it? Certainly, collapse occurs by the point of detection (we should agree on that even if you think it already happened earlier). I suggested previously that no experiment can settle this question, and am wondering if there are techniques that could expose more.

If your position were correct, might there be a different result if the PBS were changed in its position (i.e. later) ? I don't expect that would happen.
As you say, I think we are in agreement on almost everything, with the one outstanding issue being whether or not it matters if the A & D photons are detected before or after the PBS. I am working on a less complicated thought experiment that may help shed some light on this, but I want to make sure I understand what I am talking about first.

SpectraCat
If hermitian operators $$H_A$$ and $$H_B$$ commute,
then
$$e^{-iH_A\tau_A/\hbar}e^{-iH_B\tau_B/\hbar}=e^{-iH_B\tau_B/\hbar}e^{-iH_A\tau_A/\hbar}$$.

Operators on different subsystems always commute.
Therefore it doesn't matter whether you interact with photons 1&2 first or photons 3&4.
Hmmm .. I appreciate your point, but it's not immediately clear to me how that translates to the entangled pairs in this example.

If we call 1&2 and 3&4 the initially entangled pairs, the measurements are carried out on 1&4 and 2&3. So, in that case, what are the subsystems? A measurement on 1 affects 2 (and vice versa), and a measurement on 3 affects 4 (and vice versa). The separability does not seem so clear in this case.

Gold Member
OK, now here is my take on what happens at the PBS:

Coming into the PBS is a stream which can be thought of as H> + V>. The H and V components are moving together. Each has a probability amplitude of .5.

Exiting the PBS are 2 separate streams: One H> and one V>. Each has a probability amplitude of .5. However, they are no longer moving together. They have been separated. But no collapse has occurred.

The separated components can be reassembled. Collapse occurs upon detection.

Thoughts? I think this is essentially a restatement of the formalism.

If we call 1&2 and 3&4 the initially entangled pairs, the measurements are carried out on 1&4 and 2&3. So, in that case, what are the subsystems? A measurement on 1 affects 2 (and vice versa), and a measurement on 3 affects 4 (and vice versa). The separability does not seem so clear in this case.
Well the Hilbert space for the photons is basically $${\mathcal H}_{ph} = \mathbb C^2\otimes\mathbb C^2\otimes{\mathbb C}^2\otimes{\mathbb C}^2$$. Whether or not the states are entangled or not is irrelevant to whether operators on this space commute. I can guarantee that $$\mathbf 1 \otimes H_2 \otimes H_3 \otimes \mathbf 1$$ commutes with $$H_1\otimes\mathbf 1 \otimes \mathbf 1\otimes H_4$$, and so in a unitary evolution, it doesn't matter which 'happens' first.

I believe in the analysis of this experiment, the approximation is that the action of the Polarising Beam Splitter is purely an operator on this space. If the PBS actually performs a measurement of some sort, then the system which should be analysed quantum mechanically is really $${\mathcal H}_{ph}\otimes{\mathcal H}_{PBS}$$.

I don't know anything about optics, so I have no idea how a PBS works (nor have I devoted enough time to really working out what situation you are all discussing!). But I believe the assumption is that the quantum mechanical state of the PBS is sufficiently undisturbed by its interaction with the photons that the interaction hamiltonian is well approximated by an operator which acts purely on the photon space.

Edit: just noticed Dr Chinese's reply: My thoughts? I don't believe in collapse! (And I realise I should read what the experiment is. I wish it was all in the language of spins, I don't care much for the various bits of optical equipment)

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SpectraCat
OK, now here is my take on what happens at the PBS:

Coming into the PBS is a stream which can be thought of as H> + V>. The H and V components are moving together. Each has a probability amplitude of .5.

Exiting the PBS are 2 separate streams: One H> and one V>. Each has a probability amplitude of .5. However, they are no longer moving together. They have been separated. But no collapse has occurred.

The separated components can be reassembled. Collapse occurs upon detection.

Thoughts? I think this is essentially a restatement of the formalism.
Actually, I am glad you posted this .. I had been thinking of a PBS more in terms of a polaroid filter ... but of course your description is more correct. The polarization entanglement of the photon becomes a "which-way" entanglement of the PBS arms, and I agree that in this case it is quite plausible that there is no "collapse" (I really don't like that term) until the photon interacts with the detector in one arm or the other. It also seems plausible that the initial entangled state might be reconstructed by recombining the two paths through a second, reversed PBS. I expect there might be a phase matching condition that makes such a construction impractical, but I can't think of a theoretical reason why it shouldn't be possible.

However, I think the problem is significantly more complex in the case we are discussing, because here there are two inputs to the FBS (fiber beam splitter .. actually, I am still a little fuzzy on precisely what that is, and how it relates to a standard PBS), and each input receives a photon from the separately entangled pairs. These photons now each undergo "which-way" entanglement after the FBS, and somehow are jointly detected later. Actually, this raises some questions for me about this whole setup ... for example, it is not clear to me how one can be sure that both photons could not end up in the same arm after the FBS.

So perhaps we are (or maybe just "I am") proceeding towards enlightenment, but I still have a hard time envisioning how the entanglement swapping could work if the initial entangled pairs have "undergone decoherence" (I prefer that to collapsed), due to measurement of the non-interacting members of the pairs (A & D). I still think that in that case, the states of the interacting photons (B & C) are completely determined before they enter the FBS, and so they cannot become entangled, any more than any other "independent" photons for which we have complete state information could become entangled.

Demystifier
Gold Member
If hermitian operators $$H_A$$ and $$H_B$$ commute,
then
$$e^{-iH_A\tau_A/\hbar}e^{-iH_B\tau_B/\hbar}=e^{-iH_B\tau_B/\hbar}e^{-iH_A\tau_A/\hbar}$$.

Operators on different subsystems always commute.
Therefore it doesn't matter whether you interact with photons 1&2 first or photons 3&4.
Exactly!

Demystifier
Gold Member
I think that Demystifier's post does not really resolve anything
I think it depends on what exactly the problem to be resolved is. For example, for those who insist that the collapse should be viewed as a true objective event, my post does not resolve much. But for those who are ready to adopt some variant of many-world or Bohmian interpretation, it resolves a lot.

SpectraCat
I think it depends on what exactly the problem to be resolved is. For example, for those who insist that the collapse should be viewed as a true objective event, my post does not resolve much. But for those who are ready to adopt some variant of many-world or Bohmian interpretation, it resolves a lot.
What did you think I was talking about? I meant (obviously I thought) that it does not clearly resolve any issue in the discussion I have been having with DrChinese.

Just for the record, I *never* used the term "collapse" before in my arguments ... I always avoid it because of the associated "measurement problem" baggage. DrChinese drastically reduced my arguments and put that word in my mouth .. I eschew it totally.

And finally, posts like your last one are basically proselytizing, and are very hard to take. First of all, it is completely devoid of content or relevance to this thread, and second, the implication is that there are a group of poor confused souls out there, sullied and tainted by the evil stain of the Copenhagen interpretation (or whatever), who could be Saved if only they would see the light of the great and powerful Bohmian interpretation (or whatever). Give me a break.

You are of course entitled to your point of view, but can we please keep the "religion of interpretations" out of this thread, and get back to the subject at hand?

SpectraCat, here is a start of the thread:

SpectraCats says: collapse of the wave function occurs at the PBS.
I say: the photon must be detected after the PBS for collapse to occur.
How can you discuss the subject avoiding the question 'what is a collapse'?
So Demistifier is right.

But you can reformulate the original question in terms of macroscopic realism, asking only about macroscopic observables (like what the hand of voltmeter will indicate?), avoiding the word 'collapse'.

Demystifier
Gold Member
You are of course entitled to your point of view, but can we please keep the "religion of interpretations" out of this thread, and get back to the subject at hand?
What I don't understand is what, if not the issue of collapse, the subject of this thread is?

Gold Member
What I don't understand is what, if not the issue of collapse, the subject of this thread is?
You're both correct about the subject of the thread! It is both about collapse in this particular case, as well as the physical (or not) nature of collapse. I think this is a great example to probe what collapse really means. Maybe there is no such thing, but nonetheless all we ever see is one outcome.

Demystifier
Gold Member
It is both about collapse in this particular case, as well as the physical (or not) nature of collapse.
I think you can say nothing about the former before saying something general about the latter. Moreover, I think that when you adopt some general answer on the latter, the former becomes trivial.

Or to quote Einstein:
"I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts; the rest are details."

I think you can say nothing about the former before saying something general about the latter. Moreover, I think that when you adopt some general answer on the latter, the former becomes trivial.

Or to quote Einstein:
"I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts; the rest are details."
Every debate cannot come down to dBB vs. The World... or Interpretations. This is nuts and bolts, not gods and monsters.

SpectraCat
SpectraCat, here is a start of the thread:

How can you discuss the subject avoiding the question 'what is a collapse'?
So Demistifier is right.

But you can reformulate the original question in terms of macroscopic realism, asking only about macroscopic observables (like what the hand of voltmeter will indicate?), avoiding the word 'collapse'.
For crying out loud, read my posts .. I NEVER SAID ANYTHING ABOUT COLLAPSE, EVER. And furthermore, I did not ever make the statement that was attributed to me in DrChinese's post. Read my first response in this thread for my full argument.

Yes, I talked about destruction of the entangled state by the measurement of the "non-interacting" A & D photons. The entire issue boils down to the following in my view:

Does the detection of the A & D photons really instantaneously destroy their respective entangled states with B and C? If it does, and their detection occurs before B and C enter the fiber beam splitter, then I cannot see how there is any entanglement left that can be "teleported" to A & D. To me it seems that in this case, at the time they enter the beam splitter, B & C are equivalent to any other pair of independent photons with completely specified polarization states, and so there can be no polarization entanglement after they have interacted with the fiber beam splitter.

DrChinese's position, as far as I understand it, is that the detection of A & D does not completely destroy the initial entangled states in this experiment, whatever the state of B & C relative to the fiber beam splitter, because the full experiment has not yet been completed, and the situation is only resolved after the measurement of the B & C photons.

These two views provide testably different predictions, i.e. whether or not there should be a Bell inequality violation for the A & D photons, in the specific case where the detection of A & D temporally precedes the entrance of the B & C photons into the fiber beamsplitter. I have searched through the literature for an experiment that *explicitly* covers this case, but so far I have not found it. Even lacking such experimental verification, I am willing to accept that my position is wrong, but not until it has been made clear to me *why* it is wrong, in a manner that covers the details of this particular experiment. Blanket statements like "order of measurements doesn't matter" are too opaque for me in this case, because I cannot see how they can be applied in the context of this experiment.

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SpectraCat
What I don't understand is what, if not the issue of collapse, the subject of this thread is?
The post I criticized did not add anything to the discussion of "collapse" ... it was only about whether or not someone (presumably me) was "ready to adopt some variant of many-world or Bohmian interpretation" (your words). It was also based on a quote by me that was taken COMPLETELY out of context. That is why it got the reaction that it did.

DrChinese mis-stated my position in his initial post ... read my first response in this thread if you want my take on the subject of this thread.

Gold Member
Does the detection of the A & D photons really instantaneously destroy their respective entangled states with B and C? If it does, and their detection occurs before B and C enter the fiber beam splitter, then I cannot see how there is any entanglement left that can be "teleported" to A & D. To me it seems that in this case, at the time they enter the beam splitter, B & C are equivalent to any other pair of independent photons with completely specified polarization states, and so there can be no polarization entanglement after they have interacted with the fiber beam splitter.

DrChinese's position, as far as I understand it, is that the detection of A & D does not completely destroy the initial entangled states in this experiment, whatever the state of B & C relative to the fiber beam splitter, because the full experiment has not yet been completed, and the situation is only resolved after the measurement of the B & C photons.

These two views provide testably different predictions, i.e. whether or not there should be a Bell inequality violation for the A & D photons, in the specific case where the detection of A & D temporally precedes the entrance of the B & C photons into the fiber beamsplitter. I have searched through the literature for an experiment that *explicitly* covers this case, but so far I have not found it. Even lacking such experimental verification, I am willing to accept that my position is wrong, but not until it has been made clear to me *why* it is wrong, in a manner that covers the details of this particular experiment. Blanket statements like "order of measurements doesn't matter" are too opaque for me in this case, because I cannot see how they can be applied in the context of this experiment.
You have my position correct. Until the full context (experiment) is specified, there are still possibilities that "seem" to defy logic. But they don't defy the QM formalism, and the results can be predicted using QM. And those results will show that regardless of time ordering, A & D can show "perfect" correlations indicative of entanglement. However, the correlations are dependent on the type of entanglement that occurs, which is in turn dependent on the B & C PBS outcomes.

Keep in mind that there is an alternative experiment that can be performed on B & C. You could, instead of running them through a common PBS, run each through a separate PBS. In that case, A & D would NOT be entangled. That decision can be made AFTER A & D are detected. Strange as it seems...

Demystifier