Entanglement when I "produce" positron-electron pairs one at a time

[metastable]

Suppose I "produce" positron-electron pairs one at a time (by produce I mean in plain language the inverse of annihilation). Next I measure the vector of the magnetic moment of each positron. Is each pair that is produced entangled? Without measuring the electrons, can I now be much more certain of each of their magnetic moment vector values?

 

[DrChinese]

Is each pair that is produced entangled?

Yes, such pairs would be entangled.

 

[Nugatory]

Suppose I "produce" positron-electron pairs one at a time (by produce I mean in plain language the inverse of annihilation).

The term you’re looking for is “pair production”

Without measuring the electrons, can I now be much more certain of each of their magnetic moment vector values?

I'm not understanding the question... if you aren't going to measure them what can you expect to know? If you do measure them, you'll get the results you'd expect from conservation of angular momentum: measure the spins on the same axis and they'll be opposite.

 

[metastable]

I'm not understanding the question... if you aren't going to measure them what can you expect to know?

Suppose I'm studying the way electrons scatter in collisions with other electrons, can I make more accurate predictions in advance about the scattering than otherwise possible, if both of the electrons involved were produced via pair production, and the corresponding positrons were also both measured to determine the orientation of their magnetic moment vectors?

 

[Nugatory]

can I make more accurate predictions in advance about the scattering than otherwise

Perhaps. It will depend on the details of the interactions.

 

[DrChinese]

Suppose I'm studying the way electrons scatter in collisions with other electrons, can I make more accurate predictions in advance about the scattering ...

No additional information is gained. It's essentially redundant.

 

[metastable]

No additional information is gained. It's essentially redundant.

So if I understand correctly, if the unmeasured electrons are fired towards a double slit, there will be interference patterns.

 

[DrChinese]

So if I understand correctly, if the unmeasured electrons are fired towards a double slit, there will be interference patterns.

Entangled particles do not normally produce an interference pattern as you might otherwise expect. If they did, that attribute could be exploited to send (FTL) signals.

 

[metastable]

Entangled particles do not normally produce an interference pattern as you might otherwise expect. If they did, that attribute could be exploited to send (FTL) signals.

I don't understand. Are you saying the "produced" & "entangled" electrons A) "won't ever produce an interference pattern," or B) "won't ever produce an interference pattern, if I measure the corresponding entangled positrons" or C) "will still produce an interference pattern, as long as I do not measure the corresponding positrons"

 

[DrChinese]

I don't understand. Are you saying the "produced" & "entangled" electrons A) "won't ever produce an interference pattern," or B) "won't ever produce an interference pattern, if I measure the corresponding entangled positrons" or C) "will still produce an interference pattern, as long as I do not measure the corresponding positrons"

See the reference, figure 2, S290. It's a somewhat complicated subject explaining the why of it, and my explanation tends to oversimplify. But basically the source is not coherent (a requirement to get interference). And if you make it coherent, it won't be entangled.

https://pdfs.semanticscholar.org/3644/6f15507880c629e06391adf9d21aa6d76015.pdf

 

[metastable]

It says:

“Because of the perfect corre- lation between the two particles, particle 2 can serve to find out which slit particle 1 passed and therefore no interference pattern arises.”

I’m confused on this point, does it mean A) only if we look at particle 2, then particle 1 does not produce an interference pattern or B) entangled electrons never produce an interference pattern, even if we don’t look at particle 2

 

[DrChinese]

It says:

“Because of the perfect corre- lation between the two particles, particle 2 can serve to find out which slit particle 1 passed and therefore no interference pattern arises.”

I’m confused on this point, does it mean A) only if we look at particle 2, then particle 1 does not produce an interference pattern or B) entangled electrons never produce an interference pattern, even if we don’t look at particle 2

B is correct. Of course, you CAN make them coherent so that they produce an interference pattern, but then they are no longer entangled.

 

[metastable]

If I understand you correctly, newly “created” electrons won’t produce an interference pattern in a double slit experiment. In order to observe an interference pattern with electrons fired one by one in a double slit experiment, each newly created electron must be modified before the experiment in such a way that the quantum state which it is in is termed “coherent.”

 

[DrChinese]

If I understand you correctly, newly “created” electrons won’t produce an interference pattern in a double slit experiment. In order to observe an interference pattern with electrons fired one by one in a double slit experiment, each newly created electron must be modified before the experiment in such a way that the quantum state which it is in is termed “coherent.”

Close enough. Keep in mind this is a complex subject with nooks and crannies (both entanglement and coherence). In overly simplistic terms, coherence and entanglement are complementary: more of one means less of the other. You can read a little about coherence here:

https://en.wikipedia.org/wiki/Coherence_(physics)#Quantum_coherence

 

[vanhees71]

Entangled particles do not normally produce an interference pattern as you might otherwise expect. If they did, that attribute could be exploited to send (FTL) signals.

Can you elaborate on this? I'm puzzled. I don't understand both claims.

The only thing you need to get interference effects at a double slit is that your wave packet is broad enough in space and sharp enough in momentum.

Now consider an unstable particle at rest, e.g., a neutral pion, decaying into two particles (like $\pi^0 \rightarrow \gamma \gamma$). The uncertainty in the total energy and momentum is governed by the width of the particle's spectral function and this can be pretty small, i.e., you have pretty well-determined momenta of the decay products, i.e., the asymptotic free state of these decay products are pretty close to plane waves and thus you can easily do interference experiments with them. E.g., you can send one of the photons through a double slit and repeating this often enough there'll occur an interference pattern. Of course this won't in any way instantaneously affect the other photon though it's entangled (in both momentum and polarization). This is guaranteed by the locality of the QFT (in this case QED) describing the interaction of the photon with the double slit. There's thus also no way to communicate in this with any faster-than light signal.

Another example is parametric down conversion. There you have also momentum and polarization entangled photons, and plenty of interference experiments, including the very fascinating quantum-eraser experiments have been done with them, all with the result that quantum theory is bang on right with its predictions about the behavior of these entangled photon pairs. The only reason why usually experiments are done with parametric-down conversion produced photons rather than using particle decays (or atomic transitions as in the early days of Bell measurements as in the pioneering experiment by Aspect) is that it's way more efficient to produce entangled photon states.

 

[DrChinese]

Can you elaborate on this? I'm puzzled. I don't understand both claims.

The only thing you need to get interference effects at a double slit is that your wave packet is broad enough in space and sharp enough in momentum.

...

Another example is parametric down conversion. There you have also momentum and polarization entangled photons, and plenty of interference experiments, including the very fascinating quantum-eraser experiments have been done with them, all with the result that quantum theory is bang on right with its predictions about the behavior of these entangled photon pairs. The only reason why usually experiments are done with parametric-down conversion produced photons rather than using particle decays (or atomic transitions as in the early days of Bell measurements as in the pioneering experiment by Aspect) is that it's way more efficient to produce entangled photon states.

For reference on this, see post #10 from Zeilinger.

If you were able to know which slit a particle passed through on side A, then that would tell you which slit it passed through on the other (side B). Presumably there would be no interference on side B in that case. You could signal from A to B by choosing to observe the slits on side A (resulting in no interference at B) or not (resulting in interference at B).

No question that QM is "bang on" right, nor that PDC does produce interference effects when you perform coincidence counting. But I believe that to get an interference effect on one side alone (no coincidence counting), you must first run the photons through a single slit or similar (which stops entanglement on the momentum basis).

Did we have a discussion on a related subject previously? It seems to me you showed me a few things about coherence at some point. If so, perhaps the OP would benefit from your answer to the questions.

 

[vanhees71]

No, this is not correct. You cannot communicate faster than light in this way via entangled photons. You need to exchange the information about through which slit photon A came to also erase the interference pattern at site B. There is no causal interaction between the measurement processes if the measurement events are space-like separated. Entanglement describes (stronger-than-classical) correlations of properties but cannot provide causal connections between space-like separated events. That's all in relativistic QFT by construction since microcausality is built in. Of course, it's worth while to analyze this in each particular experiment.

The article by Zeilinger is a bit sloppily formulated, and thus this becomes clear only through careful reading. The key sentence is [empasis mine]:

"Therefore, a double-slit interference pattern for photon 2 is registered conditioned on registration of photon 1 in the focal plane of the lens."

You need to choose a subensemble of the photon 2 preparation conditioned on registration of photon 1, i.e., you need to provide the information about the detection of photon 1 to decide whether you choose to register photon 2 or not. This information can only be provided with a signal that is not faster than the speed of light. For details, also see the excellent PhD thesis by Dopfer

http://www.univie.ac.at/qfp/publications/thesis/bddiss.pdf

I'm afraid there's no English translation though :-((.

 

[DrChinese]

No, this is not correct. You cannot communicate faster than light in this way via entangled photons. You need to exchange the information about through which slit photon A came to also erase the interference pattern at site B. There is no causal interaction between the measurement processes if the measurement events are space-like separated. Entanglement describes (stronger-than-classical) correlations of properties but cannot provide causal connections between space-like separated events. That's all in relativistic QFT by construction since microcausality is built in. Of course, it's worth while to analyze this in each particular experiment.

The article by Zeilinger is a bit sloppily formulated, and thus this becomes clear only through careful reading. The key sentence is [empasis mine]:

"Therefore, a double-slit interference pattern for photon 2 is registered conditioned on registration of photon 1 in the focal plane of the lens."

You need to choose a subensemble of the photon 2 preparation conditioned on registration of photon 1, i.e., you need to provide the information about the detection of photon 1 to decide whether you choose to register photon 2 or not. This information can only be provided with a signal that is not faster than the speed of light. For details, also see the excellent PhD thesis by Dopfer

http://www.univie.ac.at/qfp/publications/thesis/bddiss.pdf

I'm afraid there's no English translation though :-((.

Yes, I'm familiar with all that... which is exactly what I said. Repeating: entangled photons do NOT produce an interference pattern without coincidence counting (conditional registration). And no FTL signal is possible either.

And since you brought it up: I certainly agree there is no causal connection between space-like separated events. The obvious reason that is the case (which many physicists reject) is that reality is not causal (from past to future).

I don't have anything further to add that might help the OP. Is there anything the OP said above that needs further clarification?

 

[vanhees71]

Yes, I'm familiar with all that... which is exactly what I said. Repeating: entangled photons do NOT produce an interference pattern without coincidence counting (conditional registration). And no FTL signal is possible either.

Ok, then I misunderstood you before. We agree on that.

And since you brought it up: I certainly agree there is no causal connection between space-like separated events. The obvious reason that is the case (which many physicists reject) is that reality is not causal (from past to future).

I hope that is a typo, because otherwise I'm totally confused about your opinion. The last sentence should read

The obvious reason that is the case [...]] is that reality is causal.

I.e., the word "not" must not be there!

That's what all the fuss is about this apparent faster-than-light communication through entangled quantum systems: All of physics must be causal, because otherwise physics is obsolete. We can't have physics and an acausal reality since this was a contradiction in itself.

This has the immediate consequence that any spacetime model must contain a causality structure, i.e., it must be clear which events can be causally connected an which not, and this must be frame independent. In special relativity only events separated by time- or light-like vectors can be causally connected and this, by the very construction of Minkowski space is a frame-independent statement.

Applied to measurements on entrangled quantum systems the idea of an apparent tension between relativistic causality structure and quantum theory solely originates from the collapse postulate, according to which a measurement is claimed to lead to a collapse of the state of the system, and this means that a local measurement at a place A on one part of the quantum system immediately is claimed to cause an effect at a far distant place where another entangled part of the quantum system is observed.

This is not the case within the minimal interpretation, which sticks to QFT as is and doesn't add an instantaneous collapse to its dynamics, as discussed above, and you agreed to that part. So in the above sentence of yours the little word "not" should not be where you've written it ;-)).

 

[DrChinese]

1. Ok, then I misunderstood you before. We agree on that.

2. I hope that is a typo, because otherwise I'm totally confused about your opinion. The last sentence should read

The obvious reason that is the case [...]] is that reality is causal.

I.e., the word "not" must not be there!

That's what all the fuss is about this apparent faster-than-light communication through entangled quantum systems: All of physics must be causal, because otherwise physics is obsolete. We can't have physics and an acausal reality since this was a contradiction in itself.

3. This has the immediate consequence that any spacetime model must contain a causality structure, i.e., it must be clear which events can be causally connected an which not, and this must be frame independent. In special relativity only events separated by time- or light-like vectors can be causally connected and this, by the very construction of Minkowski space is a frame-independent statement.

1. Yay!

2. Ha, I meant the word NOT. It is standard physics post-Bell that either there are FTL influences, or realism/causality fails (at least a la EPR). Responding to your comment: "Entanglement describes (stronger-than-classical) correlations of properties but cannot provide causal connections between space-like separated events" I was attempting to agree with your apparent take on that. (Note that I was not attempting to push a retrocausal perspective.) I was just saying the obvious, which is that entanglement effects have no clear causal direction, and lack any element which would explain why a particular outcome occurs in a specific case. That statement should not be controversial in any way. Other than by assumption (which you and many/most are willing to make), there is no evidence which would contradict this. And so I would repeat: Reality is not causal. And physicists have been living with that possibility for nearly 100 years without being worse for the wear in day to day efforts. It is, of course, confusing that things work as they do.

3. This might be desirable, sure, but most/all models of relativity are time symmetric and lack a preferred time direction.

 

[Mentz114]

[..]
I was just saying the obvious, which is that entanglement effects have no clear causal direction, and lack any element which would explain why a particular outcome occurs in a specific case. That statement should not be controversial in any way. Other than by assumption (which you and many/most are willing to make), there is no evidence which would contradict this.

Yay !

I don't see any serious disharmony with @vanhees71 's position, maybe just an adjustment required.

 

[PeterDonis]

I certainly agree there is no causal connection between space-like separated events.

In quantum field theory, it does not have to be the case that there is no causal connection between spacelike separated measurements. All that has to be the case is that the measurements must commute: their results cannot depend on the order in which they are made.

Discussions of the Bell inequalities and EPR experiments that do not recognize this point are leaving out something important, IMO.

 

[kurt101]

In quantum field theory, it does not have to be the case that there is no causal connection between spacelike separated measurements. All that has to be the case is that the measurements must commute: their results cannot depend on the order in which they are made.

But doesn't this statement (measurements must commute) apply to the operators used in calculating the probability and does not necessarily apply to actual measurements?

 

[PeterDonis]

doesn't this statement (measurements must commute) apply to the operators used in calculating the probability and does not necessarily apply to actual measurements?

It means exactly what I said: that the results of spacelike separated measurements cannot depend on the order in which they are made. When applied to operators, it means the operators corresponding to spacelike separated measurements must commute.

I'm not sure what you mean by "does not necessarily apply to actual measurements". What other kind of measurements would it apply to?

 

[vanhees71]

1. Yay!

2. Ha, I meant the word NOT. It is standard physics post-Bell that either there are FTL influences, or realism/causality fails (at least a la EPR). Responding to your comment: "Entanglement describes (stronger-than-classical) correlations of properties but cannot provide causal connections between space-like separated events" I was attempting to agree with your apparent take on that. (Note that I was not attempting to push a retrocausal perspective.) I was just saying the obvious, which is that entanglement effects have no clear causal direction, and lack any element which would explain why a particular outcome occurs in a specific case. That statement should not be controversial in any way. Other than by assumption (which you and many/most are willing to make), there is no evidence which would contradict this. And so I would repeat: Reality is not causal. And physicists have been living with that possibility for nearly 100 years without being worse for the wear in day to day efforts. It is, of course, confusing that things work as they do.

3. This might be desirable, sure, but most/all models of relativity are time symmetric and lack a preferred time direction.

I always fall in this trap :-(. I always fail to translate the word "realism" from my standard every-day meaning, to describe what's real in the sense of the natural sciences, i.e., what's objectively observed in nature, while you used it in the philosophical sense, where it means "classical deterministic worldview", i.e., the contrary to what's really realistic. The very reason why we physicists where forced out of the paradais of the classical world view in the hard realism of QT is precisely that the classical world view is wrong (or at least an emergent phenomenon from the underlying quantum dynamics).

I disagree about your statement that "entanglement effects have no clear causal connection". This is for sure wrong either since entanglement usually has a cause, i.e., in the very beginning of an experiment something was prepared in a way which leads to entanglement (an be it only to wait that some particle decays, producing two (or more) momentum-entangled particles).

What's not causal is the collapse hypothesis (at least in its naive form). Indeed, a local interaction on one entangled particle doesn't instantaneously change the other particle's state. There are only correlations, and these have their cause clearly in the past when the entangled state was prepared, but not in the later local measurements on the single particles within the corresponding two- (or even multi-)particle state.

 

[vanhees71]

Yay !

I don't see any serious disharmony with @vanhees71 's position, maybe just an adjustment required.

It only underlines the problem to communicate about QT in a clear way. Again our understanding was undermined by using philosophical gibberish instead of clear physics language. As I more and more find confirmed: Philosophy can do great harm to the natural sciences :-(.

 

[vanhees71]

In quantum field theory, it does not have to be the case that there is no causal connection between spacelike separated measurements. All that has to be the case is that the measurements must commute: their results cannot depend on the order in which they are made.

Discussions of the Bell inequalities and EPR experiments that do not recognize this point are leaving out something important, IMO.

Can you elaborate on this? I don't see how your statement is compatible with the very foundations of QFT. Don't we choose the usual local microcausal QFTs (restricting ourselves to the unitary irreducible representations of the proper orthochronous Poincare group with $m^2 \geq 0$) to build QT-models for relativistic particles?

The measurements on several single particles in an entangled multi-particle state at far distances then cannot affect each other in an instantaneous way.

 

[stevendaryl]

Let me try to illustrate my understanding of the issue with entanglement and interference. Consider the following experimental setup:

You produce an electron at point A. From there it can take one of the following paths:

1. Travel from A to B and emit a photon and then travel to C and finally to D, where it is detected.
2. Same as path 1, except that it goes from C to E, where it is detected.
3. Travel from A to G and emit a photon and then travel to F and finally to D.
4. Same as path 3, except after F it travels to E.

Assume that at each decision point, A, C and F, the electron has a 50/50 chance of going in either direction.

Ignoring the photons, then the amplitude for the electron to be detected at D would involve interference between paths ABCD and AGFD. The amplitude for the electron to be detected at E would involve interference between paths ABCE and AGFE.

Let's assume that amplitudes are such that, without the photons, the probability would be 0% chance of arriving at D and 100% chance of arriving at E.

If there is no interference, then there is an equal probability of the electron being detected at D or E. So in the absence of interference, there is a 50/50 chance of the electron being detected at D or E. With interference, there is a 0/100 chance.

Entanglement is involved because whether you see the interference or not depends on what is done with the photon. The photon is entangled with the electron. If you measure the photon in such a way that it is possible to determine whether it came from B or G, then that gives "which path" information, and that will destroy the interference pattern. If instead, you erase the "which path" information (by routing the photon from B or G to the same final destination, where information about where it came from is lost), then you restore the interference.

What I don't understand about this type of experiment is the timing. If whether there is interference or not depends on what happens to the photons, it seems that you could delay measuring the photons until after the electron is detected. But by then, the interference or lack of interference would have already come into play.

 

[vanhees71]

In this way you cannot say anything, because you don't know the states of the electron and the photon. You have to clearly define the specific experiment you are doing. Otherwise we cannot analyze it.

 

[stevendaryl]

In this way you cannot say anything, because you don't know the states of the electron and the photon. You have to clearly define the specific experiment you are doing. Otherwise we cannot analyze it.

I'm not asking you to analyze it. I'm explaining why entanglement is relevant to whether interference patterns are seen, or not. You can fill in the details yourself, if you care enough.

 

[Mentz114]

[..]

Entanglement is involved because whether you see the interference or not depends on what is done with the photon. The photon is entangled with the electron. If you measure the photon in such a way that it is possible to determine whether it came from B or G, then that gives "which path" information, and that will destroy the interference pattern. If instead, you erase the "which path" information (by routing the photon from B or G to the same final destination, where information about where it came from is lost), then you restore the interference.

What I don't understand about this type of experiment is the timing. If whether there is interference or not depends on what happens to the photons, it seems that you could delay measuring the photons until after the electron is detected. But by then, the interference or lack of interference would have already come into play.

I think I can see what you're saying but not sure about the conclusion.

Single photon interference is shown by the two-point zero-order correlation of the single-photon state, as observed.
For the two-photon state the correlations are there in higher orders as well. ( see Ballentine page 560, chapter 19).

But entangled photons are in a singlet-state which shows no interference but a huge correlation.

The Hong-Ou-Mandel experiment (I think) predicts the equivalent.

I could be misinterpreting what I'm reading, though.

 

[stevendaryl]

I'm not asking you to analyze it. I'm explaining why entanglement is relevant to whether interference patterns are seen, or not. You can fill in the details yourself, if you care enough.

Abstractly, we can describe the situation this way:

We have an initial state $|A, -\rangle$. We have intermediate states $|C, B\rangle$ and $|F,G\rangle$. We have final states $|D,B\rangle$, $|D,G\rangle$, $|E,B\rangle$ and $|E,G\rangle$. The first component of the composite state is the state of the electron, and the second is the state of the photon (the $-$ in the initial state is because there is no photon in that state).

The interaction is such that:

$|A\rangle \rightarrow \lambda_{DB} |D,B\rangle + \lambda_{DG} |D,G\rangle + \lambda_{EB} |E,B\rangle + \lambda_{EG} |E,G\rangle$

where the various $\lambda$s are determined by the details of the experiment.

If states $G$ and $B$ of the photon are macroscopically distinguishable, then there will be probabilities:

1. $|\lambda_{DB}|^2$ is the probability that the electron will be detected at $D$ and the photon will be measured to have come from $B$
2. $|\lambda_{DG}|^2$ is the probability that the electron will be detected at $D$ and the photon will be measured to have come from $G$
3. $|\lambda_{EB}|^2$ is the probability that the electron will be detected at $E$ and the photon will be measured to have come from $B$
4. $|\lambda_{EG}|^2$ is the probability that the electron will be detected at $E$ and the photon will be measured to have come from $G$

The probability of detecting the photon at $D$ is given by: $P_D = |\lambda_{DB}|^2 + |\lambda_{DG}|^2$. The probability of detecting the photon at $E$ is given by: $P_E = |\lambda_{EB}|^2 + |\lambda_{EG}|^2$. The fact that you square and then sum shows that there is no interference.

On the other hand, let's suppose that you erase the information about where the photon came from. The way you can do that is by having some final state $Z$ for the photon which is reachable from both $B$ and $G$. Letting $\lambda_{BZ}$ be the amplitude for the photon to make a transition from state $B$ to state $Z$ and letting $\lambda_{GZ}$ be the amplitude for the photon to make a transition from state $G$ to state $Z$, then the amplitude for the composite system to end up in state $|D,Z\rangle$ is:

$\lambda_{DG}\lambda_{GZ} + \lambda_{DB} \lambda{BZ}$

and the amplitude for the composite system to end up in state $|E,Z\rangle$ is similarly

$\lambda_{EG}\lambda_{GZ} + \lambda_{EB} \lambda{BZ}$

So in this alternative experiment, where the information about where the photon came from is erased, the probability of detecting the electron at $D$ is:

$P_D = |\lambda_{DG}\lambda_{GZ} + \lambda_{DB} \lambda{BZ}|^2$

and the probability of detecting the electron at $E$ is:

$P_E = |\lambda_{EG}\lambda_{GZ} + \lambda_{EB} \lambda{BZ}|^2$

In this experiment, where the electron state is not entangled with the final photon state, there is interference.

 

[stevendaryl]

I think I can see what you're saying but not sure about the conclusion.

Single photon interference is shown by the two-point zero-order correlation of the single-photon state, as observed.
For the two-photon state the correlations are there in higher orders as well. ( see Ballentine page 560, chapter 19).

But entangled photons are in a singlet-state which shows no interference but a huge correlation.

The Hong-Ou-Mandel experiment (I think) predicts the equivalent.

I could be misinterpreting what I'm reading, though.

In the experiment I'm talking about, it's not a two-photon entangled state. The state of the photon is entangled with the state of the electron.

 

[Mentz114]

In the experiment I'm talking about, it's not a two-photon entangled state. The state of the photon is entangled with the state of the electron.

I've just seen your follow-up post.

 

[vanhees71]

I'm not asking you to analyze it. I'm explaining why entanglement is relevant to whether interference patterns are seen, or not. You can fill in the details yourself, if you care enough.

You cannot discuss this without defining which experiment is done. Are you talking about the experiment by Dopfer, Zeilinger, et al? Then it's all quite easy to describe by QED, and it's well understood under which setup and for which partial ensembles you see an interference pattern in the single-photon observations or not. To say in the very general "entanglement is relevant to whether interference patterns are seen or not" is an empty phrase.