# Measurement of entangled particles causes dechorence at a distance?

kaplan
If we entangle particles and separate them by a large distance, can the action of measuring one cause decoherence at the other's location?

If yes then does this violate relativisitic causality? Could we not use this process to transmit information instantaneously?

If no then why not? Is there a fundamental difference between the process of direct measurement of the local particle and the indirect measurement of the distant particle? Is decoherence any observer relative phenomena?

If you use the Many Worlds Interpretation of QM, the answer to this question becomes crystal clear. Nothing violates causality - all interactions and influences are completely local.

Here's how it works. When you measure particle A, the measurement changes the state of detector A. It has no effect on the state of particle B or detector B. The state of detector A becomes a superposition of the two possible results of the measurement.

Later, someone else measures particle B. The measurement changes the state of detector B. It has no effect on the state of particle A or detector A. The state of detector B becomes a superposition of the two possible results of the measurement.

The only thing you have to realize is the wavefunction after both measurements is (modulo some irrelevant phases) (|A measured + >|B measured - > + |A measured - >|B measured + >)/sqrt(2). If you don't see how to get that or the notation is unclear, ask and I can show all the steps. Those are the two possible "worlds", and we arrived there with no non-local influences at all. (In the Copenhagen interpretation that superposition is replaced by a density matrix.)

Mentor
If you use the Many Worlds Interpretation of QM, the answer to this question becomes crystal clear. Nothing violates causality - all interactions and influences are completely local.

Same with the Ensemble interpretation (from the paper I linked before):
'The resolution of the EPR paradox in terms of a statistical ensemble of singlet states is that an instantaneous action-at-a-distance is not required to ensure that conservation of angular momentum is maintained. That is, the choice of measurement on the left does not determine the outcome on the right but rather measurement of one spin is correlated to the other by virtue of the fact that they belong to the same sub-ensemble that retains the necessary correlation. That correlation is determined at the source by virtue of the common axis of quantization and not at the time of measurement.

In contrast, if the wave function were assumed to describe the possible states of a single EPR spin pair rather than an ensemble, the measurement of one spin state would require its distant partner to collapse into a specific state which is consistent with the measured particle.'

Basically the observation selects from an ensemble whose only elements are those with the correct spins.

Thanks
Bill

Gold Member
Zeilinger says that photons registered in the focal plane of the Heisenberg lens are associated with photons which make an interference pattern. i guess that they must be chosen in a pattern with no interference.
Why cannot we detect all the photons in the focal plane? the interference pattern would be seen in the double slit screen (and that is impossible).

We do detect all of the photons associated with those in the focal plane. But since we also detect those that are NOT associated with those in the focal plane, how do you know which is which? Coincidence counting solves that, but requires a classical information channel.

Gold Member
Maybe I am missing the whole point, but when you measure the first particle you no longer have an entangled system. The second particle is just an electron with a state. You can find out things about it or do tricky experiments or play weird games by knowing the results of the first measurements, but that is all.

Actually, I can't quite agree with the "particle with a state" part.

1. In entanglement swapping experiments, after you measure Bob, you won't have Alice in a matching state. That is because coincident with measuring Bob, you measured Chris (who is entangled with Dale). And keep in mind that the coincident measurements of Bob and Chris must be done so that you cannot distinguish Bob from Chris. Now Alice and Dale are entangled, so their state is indeterminate. They will violate a Bell Inequality.

2. You could measure Alice and Dale FIRST and get the same results.

Note that trying to convert examples such as this to a simpler description can easily become problematic. You can't really come up with a simple explanation or rule when you try to say "first measurement causes collapse". Because it really doesn't, the results actually depend on the COMPLETE context. A part of the context won't quite cut it.

kaplan
In contrast, if the wave function were assumed to describe the possible states of a single EPR spin pair rather than an ensemble, the measurement of one spin state would require its distant partner to collapse into a specific state which is consistent with the measured particle.

Actually it doesn't require that. More precisely, it requires that only if you insist there is a unique result for the measurement - i.e. that measuring devices cannot be in superpositions of different results.

But measuring devices CAN be in such states according to the Multi Worlds Interpretation, or simply according to time evolution by Schrodinger's equation applied to the measuring device.

Homework Helper
I once had the same idea (for an FTL device), and that is when I first discovered that entangled photons do not produce interference patterns.

http://www.hep.yorku.ca/menary/courses/phys2040/misc/foundations.pdf

See page S290, figure 2

Brilliant.

That page answers my question perfectly. I'm more than happy to extrapolate that explanation to my original question.

As ever, it's disturbing how QM always seems to be one step ahead. It's yet another way that our intuition from the classical world is broken.
If you look at the next figure in that article (figure 3), they show how to get the interference pattern back - by erasing the momentum information from particle 2 (P2).

If I am reading this correctly, the P2 interference pattern reappears when detection of P1 is done so that momentum information is destroyed at D1.

This would, at first appear to create the possibility of FTL information transmission from D1 to D2. (They also run a similar "communication" from D2 to D1.) That is, by modulating the position of D1, for example by pivoting a mirror to divert the P1 to either a close D1a or a more distant D1b, you could control whether an interference pattern was observed at D2.

Of course, this won't happen - simply because it's against the FTL law. But it would be interesting to see the details of how this is enforced.

On the next page, there is this very interesting remark:
By virtue of the strong momentum entanglement at the source, the other wave packet then has a related momentum distribution which actually is, according to an argument put forward by Klyshko (1988), the time reversal of the other wave packet. Thus, photon 1 appears to originate backwards from the double slit assembly (D2) and is then considered to be reflected by the wave fronts of the pump beam into the beam towards the lens ...

I'm not sure I would subscribe to that logic, but it suggests an interesting series of experiments. Let's call that UV particle P0. At a certain point in time, P0 will be approaching the splitter while virtual Klyshko particles are being "emitted" from the detectors, virtual Klyshko P1 (kP1) from D2 and kP2 from D1. So as we advance through time, P0, kP1, and kP2 all approach the splitter at speed c. If these Klyshko particles really exist, then it should be possible to mess up the results at D1 by interfering with kP1 and to mess up the results at D2 by interfering with kP2. For example, if D1 is set up for erasure, closing a shutter along kP2 path at the right moment before P0 reaches splitter should extinguish the interference pattern.

Someone try it out. I want to know what happens!

Mentor
Actually it doesn't require that. More precisely, it requires that only if you insist there is a unique result for the measurement - i.e. that measuring devices cannot be in superpositions of different results.

That's true. No actual collapse occurs in MWI - in that interpretation the reason is its described by the un-collapsed wavefunction which admits only the correct correlations in each 'world'.

Thanks
Bill

Gold Member
Actually, I can't quite agree with the "particle with a state" part.

1. In entanglement swapping experiments, after you measure Bob, you won't have Alice in a matching state. That is because coincident with measuring Bob, you measured Chris (who is entangled with Dale). And keep in mind that the coincident measurements of Bob and Chris must be done so that you cannot distinguish Bob from Chris. Now Alice and Dale are entangled, so their state is indeterminate. They will violate a Bell Inequality.

I think you "sorta cheated" by introducing a further entanglement without "really measuring" Bob in a final way. Your point is taken though. Thanks

Gold Member
We do detect all of the photons associated with those in the focal plane. But since we also detect those that are NOT associated with those in the focal plane, how do you know which is which? Coincidence counting solves that, but requires a classical information channel.

If there is a one by one bijection between the screen and the imaging plane, when we put the detector in the imaging plane we may have coincidence for all the hits on the sceen.
A part of them belong to the interference pattern which Dopfer describes. So the corres ponding photons (with interfrence) may be registerd in the focal plane , in the imaging plane and in any plane in between.
How can we separate the ones passing through the focal plane which are associated with the interference pattern?
I think we have not the notion of a photon associated with a plane after the lens.

Gold Member
If there is a one by one bijection between the screen and the imaging plane, when we put the detector in the imaging plane we may have coincidence for all the hits on the sceen.
A part of them belong to the interference pattern which Dopfer describes. So the corres ponding photons (with interfrence) may be registerd in the focal plane , in the imaging plane and in any plane in between.
How can we separate the ones passing through the focal plane which are associated with the interference pattern?
I think we have not the notion of a photon associated with a plane after the lens.

I don't understand your question. It is fundamental that some of what you are imagining does not actually occur as you picture it. That is why there is no FTL opportunity here.

Gold Member
I think that the problem may be in my bad english.
I do not think that that ftl things exist.
I believe that bob may do what he wants this wil not change the pattern Alice sees.

Please tell me what you think is incorrect:
1) when the detector is at a distance 2f of the lens (the imaging plane) all the registered
photons are corresponding to the pattern seen by Alice.
2) all these photons pass through the focal plane behind the lens.
3) if the pattern is made of 1000 hits there are 1000 photons which may be detected at any distance L of lhe lens
4) There is a sub ensemble of these 1000 photons whicch may be detected by a detector in the focal plane and by a coincidence setup they will allow Alice to construct afterwards an interference pattern.

So my question is: is it enough to put the detector in the focal plane and to have coincidence for getting the subensemble of th 1000 photons thatt will give the interferrence subpattern?

San K
This would, at first appear to create the possibility of FTL information transmission from D1 to D2. (They also run a similar "communication" from D2 to D1.) That is, by modulating the position of D1, for example by pivoting a mirror to divert the P1 to either a close D1a or a more distant D1b, you could control whether an interference pattern was observed at D2.

Of course, this won't happen - simply because it's against the FTL law. But it would be interesting to see the details of how this is enforced.

The entanglement weakens in proportion to the increase in sharpness/clarity of the interference pattern. Thus information cannot be extracted.

This necessitates the use of coincidence counter, if we want to extract information.

I think - No information is transferred during entanglement/dis-entanglement - in any case.

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Gold Member
I do not propose an experiment with ftl possibility.
I only try to understand what Zeilinger says in
see p S292:
"First, it is clearly possible to have a concept of continuous
complementarity. In our case, placing the detector of
photon 1 somewhere in between the two extreme posi-
tions mentioned will reveal partial path information and
thus an interference pattern of reduced visibility"

My questions concern these lines

San K
I do not propose an experiment with ftl possibility.
I only try to understand what Zeilinger says in

see p S292:
"First, it is clearly possible to have a concept of continuous
complementarity. In our case, placing the detector of
photon 1 somewhere in between the two extreme posi-
tions mentioned will reveal partial path information and
thus an interference pattern of reduced visibility"

My questions concern these lines

While we wait for Dr. Chinese to wake up, from his dreams of Taj Mahal, finish his wonton soup and dumplings, :) and respond, below is an attempt:

As the reliability/probability of partial path information is increased the pattern visibility is reduced and vice versa.

For example if as we increase from 50-50 probability (that the photon went through slit A)

to say

70-30 probability (that the photon went through slit A)

The visibility of the interference pattern will start to reduce in proportion.

This is due to complimentarity ...and prevents information transfer.

Gold Member
I think you are right.
My wrong idea was that among all the photons that build the real pattern it had to be a trick to get
(in the focal plane) which will give us the interference pattern.
I think now that there is an amplitude formula depending on the distance to the lens
that gives the result.

Gold Member
I found Dopfer1998 thesis.pdf
It is in german!
see p 83 She puts the detector between the focal plane (Brennebene) and the imaging plane (Abbildungsebene)
I hope that a german speaking physicist will help us.