When does entanglement actually end?

[DrChinese]

I haven't seen a paper which answers this particular question, maybe someone else has... (I have scanned the preprint archive but to no avail so far).

Most Bell tests use polarizing beam splitters (PBS) to check photons at Alice and Bob. Typical are 2 detectors at Alice and 2 at Bob. Results of all 4 are correlated and analyzed. You would normally say the entanglement ends once we know which way the photon goes through the beam splitter.

What if we takes the 2 beams at Alice and merge them back very precisely together again? I.e. such that it is no longer possible to tell which path the photon took through the PBS. I would expect that the resultant reconstructed beam (Alice) is still entangled with Bob. If you tested Alice and Bob at this point, I would expect us to see the perfect correlations and the Bell inequality violations per usual. Is this correct?

So when does the entanglement actually end? If what I am saying is right, the PBS is not actually capable of ending the entanglement itself. Instead, it is the detection of the photon - and what we know about it at that point - which ends the entanglement. I believe this is fully consistent with the QM prediction.

 

[friend]

I think all entanglement means is that the particles have become correlated unless one or both bounce off some other particle. Why is this so mysterious

 

[DaveC426913]

I think all entanglement means is that the particles have become correlated unless one or both bounce off some other particle. Why is this so mysterious

OK, so your contention is that entanglement ends when the particles collide with other particles. Is that verifiable or is it a guess?

 

[DrChinese]

I think all entanglement means is that the particles have become correlated unless one or both bounce off some other particle. Why is this so mysterious

When a particle goes through a polarizing beam splitter or a filter: as far as anyone knows there is no physical contact between the polarizer apparatus and the photon itself. I believe it is more of a field effect. Clearly, if a series of polarizers is involved, the entanglement does NOT continue in the normal case (as opposed to the special case I described in the OP). So perhaps the mechanism is simply passing through a filter...

...Except that the case I am asking about would actually mean 2 filters are involved and so would negate that conclusion (since the first PBS did not completely end the possibility of entanglement. That is what I am asking about. In other words, the end of the entanglement seems to be contingent on what we have the possibility of knowing. This implies that the underlying mechanism is not specific to one particular observational apparatus.

Besides, you can definitely bounce entangled photons off a mirror or an optical fiber and that has no apparent effect on the entangled state. This is done routinely in Bell-type experiments.

 

[peter0302]

I think you're right. It ends when there is an _irreversible_ measurement - i.e. detection - made, and when decoherence occurs. What you're talking about is like a delayed choice quantum eraser isn't it? If the measurement can be reversed, the particles can be "re-entangled" back to the state they were in before the measurement.

 

[Phrak]

Particles A and B are entangled when they are described by a single wave function. I’m not sure if it even makes sense to give them distinguishing labels like A and B, except to say what Alex might measure is not what Bobbie would measure.

If the wave passes through a beam splitter it’s entangled with the splitter, because in principle it’s possible to measure the direction it passed through the splitter due to the momentum imparted to the splitter. In measuring the momentum imparted to the beam splitter, the path of the wave is known.

If Alex measures a particle then Alex is entangled with particles A and B.

If Bobbie also measures a particle, she’s entangled with Alex.

Edit: It makes sense to say the last two statements as a third observer, observing Alex and/or Bobble. I don't know if it's correct to say, "I'm entangled with paricles A and B."

 

[DrChinese]

I think you're right. It ends when there is an _irreversible_ measurement - i.e. detection - made, and when decoherence occurs. What you're talking about is like a delayed choice quantum eraser isn't it? If the measurement can be reversed, the particles can be "re-entangled" back to the state they were in before the measurement.

Yes, I think that is always the case. Kinda odd, doesn't it seem?

 

[peter0302]

Not if you like MWI. :)

I think what you're talking about is more evidence that there's no physical link between them and that the only physical reality of entanglement is manifested when measurements are made - which is why we don't see any evidence of it unitl two measurements are compared. Regardless of what interpretation you like (collapse, decoherence, many-worlds), in all of them it's still the irreversible measurement that causes the results we see. The photon bouncing off the mirror - for which there is no evidence afterwards - isn't a measurement, so it has no effect on the "link."

 

[moving_on]

With respect to reflection, can't this 'affect' polarization in certain circumstances?
What I mean is 'polarization by reflection'.

 

[moving_on]

Thinking more about this.
My understanding is that when you set up a 'polarization by reflection' experiment, it is possible to infer the polarization of the reflected photon based on the angle set for the reflector. Is this about right? (assuming it reflects).
What about a 'cat in the box' version. We program a 'randomizer' to choose one
of a set of possible angles. We send in some photons from a stream of entangled pairs.
We don't then know the angle and hence cannot infer the polarization of the exiting photon...
... would this cause disentanglement?
There are probably lots of reasons why this is complete tosh, so I'm going to try
to stop thinking now...

 

[peter0302]

Haha. It's not trash but you need to understand some fundamentals better first. *If* you learn anything about a particle, that is a measurement. Whether it's an active measurement - like detection - or a passive measurement - like no detection - anything you do that allows you to infer a value *is* a measurement from a QM perspective. It's truly an information based theory, which is why it's so difficult to reconcile it with what we see in the macroscopic world.

 

[vanesch]

Not if you like MWI. :)

I think what you're talking about is more evidence that there's no physical link between them and that the only physical reality of entanglement is manifested when measurements are made - which is why we don't see any evidence of it unitl two measurements are compared. Regardless of what interpretation you like (collapse, decoherence, many-worlds), in all of them it's still the irreversible measurement that causes the results we see. The photon bouncing off the mirror - for which there is no evidence afterwards - isn't a measurement, so it has no effect on the "link."

Indeed, what ends *observable* entanglement is measurement. Now, in all projection-based theories observation puts the state of the observed system in a "product state", so that there is no entanglement anymore. However, in all "purely unitary" theories/interpretations/... such as MWI, measurement IS entanglement (extra entanglement, between the observer and the system state). So in one set of views, measurement ends entanglement, in another, measurement entangles further (and hopelessly irreversibly).
Both views can be reconciled by saying that *from the point of view of a particular observer* what he's entangled with is a pure product state of the system under observation.

 

[LaserMind]

By a measurement we mean getting a value for an observable...
When a wave packet is forced to reveal the values of its states in the form of observables (operators) by some external agent (another wave packet) then that paticular wave packet's state construction is ended, as are all its possible paths it may have instantly and its new wave packet has realigned states and entanglements.

But a particle spends all of its life as a wave packet, its just that the packet states keep getting realigned/entangled by 'hitting' other wave packets.

 

[peter0302]

Yeah but even you "Detect" a particle through its absence - thereby not employing a "hit" with another wave packet - that's still a quantum measurement. So actually no "interaction" in the traditional sense is required for a measurement.

 

[DrChinese]

Indeed, what ends *observable* entanglement is measurement. Now, in all projection-based theories observation puts the state of the observed system in a "product state", so that there is no entanglement anymore. However, in all "purely unitary" theories/interpretations/... such as MWI, measurement IS entanglement (extra entanglement, between the observer and the system state). So in one set of views, measurement ends entanglement, in another, measurement entangles further (and hopelessly irreversibly).
Both views can be reconciled by saying that *from the point of view of a particular observer* what he's entangled with is a pure product state of the system under observation.

Thanks as always for your keen comments. It is interesting that our entangled particles could have their entanglement ended for one commuting observable, while remaining entangled for another. I am thinking about perhaps polarization and momentum.

 

[LaserMind]

It is interesting that our entangled particles could have their entanglement ended for one commuting observable, while remaining entangled for another. I am thinking about perhaps polarization and momentum.

I agree with you that the actual collapse of the wave function (so-called) is a key concept - when, how, where, why, how long - it strikes me that it only changes to another wave function and never comes into 'our Universe' as an actual object - for example an electron is always an electron and will exist in a wave packet only.

Sometimes I get the impression, reading the literature, that it comes out of superposition as a little gray ball (or even a cat!) or something - which is not the case at all.

Also, your point about partially collapsing some states is unclear - it must impinge on entanglement considerations.

 

[peter0302]

The electron certainly doens't morph. But according to the generally accepted models right now, the electron (and the photon for that matter) is _always_ a particle. What changes is the probability distribution of where you'll detect it.

There are many problems with the idea of a wave-packet, not the least of which is that if there is a physical wave-packet, it would exist everywhere in the universe and changes in it would be instantaneous everywhere in the universe, and therefore explicitly non-local. By considering the particles as particles, the only non-local element is the probability wave, which itself has no physical meaning.

 

[Phrak]

I wouldn't pretend to know the all about entanglement, but a lot of the discussion here has been predicated upon

1) fitting the idea of entanglement into a particular interpretation of quantum mechanics without qualification,
2) what is believed constitute an interaction, and
4) the idea that an observation obtains a universal wave collapse.

When a wave passes through a beam splitter it is entangled with the splitter. An electron is entangled with the Stern-Gerlach apparatus.

When Alice observes the spin state of an entangled pair of electrons, the pair are still entangled to other observers, including Bob. What is described by one observer as a wave can be described by another oberver as a projected state.

There's a tendency to attach an objective, observer independent interpretation to various elements of quantum mechanics, but within the null interpretation, what is unclear to me, are whether variables describe what are known or what are knowable.

 

[DrChinese]

There are many problems with the idea of a wave-packet, not the least of which is that if there is a physical wave-packet, it would exist everywhere in the universe and changes in it would be instantaneous everywhere in the universe, and therefore explicitly non-local.

And yet the physical result is pretty much as if that were the case. So that is why I ask: is collapse a physical process? If it were, the about would be true.

And yet... partial collapse of the wave function could be considered a counter-argument to the above. Because now there would have to be "half-a-wave-packet" left (which would also be non-local?) to account for the results.

Yikes!

 

[peter0302]

Hehe, I can't really tell what side you're taking. :) But my answer is collapse can't be a physical process; it's just that quantum statistics don't conform to the laws of macro-statistics.

Wouldn't you rather throw out classical statistics than throw out relativity? :)

 

[LaserMind]

And yet... partial collapse of the wave function could be considered a counter-argument to the above. Because now there would have to be "half-a-wave-packet" left (which would also be non-local?) to account for the results.

Yikes!

hmmm..., re partial collapse - what make me sceptical is the 'which path' problem.
Because obtaining just one observable (partial) would reveal which path information - in say, erasure experiment - and we would then get then a 'particle' result rather than a wave interference result.
We would probably conclude the 'wave function' collapsed (for all states).

What do you think?
Mega yikes.

 

[DrChinese]

hmmm..., re partial collapse - what make me sceptical is the 'which path' problem.
Because obtaining just one observable (partial) would reveal which path information - in say, erasure experiment - and we would then get then a 'particle' result rather than a wave interference result.
We would probably conclude the 'wave function' collapsed (for all states).

What do you think?
Mega yikes.

Actually, the "partial collapse" is demonstrated as true in virtually every Bell test - although that is a by-product rather than a specific element of the Bell test.

It is normal to place filters after the PDC crystal (which is where the input photon is split into 2 output photons). These filters are tuned to a specific frequency of light because it is critical that extraneous light (of which there is a lot coming out of the PDC that is not down-converted) does not go into the detection apparatus. Those filters *absolutely* give us knowledge of wavelength, frequency and energy of the photon that passes - it is an observation! As such, there must be collapse of that part of the wavefunction. Yet... afterwards, we perform a commuting polarization observation on those same photons and notice there is perfect entanglement.

So this is not a speculative issue... partial entanglement is real.

 

[CJames]

Indeed, what ends *observable* entanglement is measurement. Now, in all projection-based theories observation puts the state of the observed system in a "product state", so that there is no entanglement anymore. However, in all "purely unitary" theories/interpretations/... such as MWI, measurement IS entanglement (extra entanglement, between the observer and the system state). So in one set of views, measurement ends entanglement, in another, measurement entangles further (and hopelessly irreversibly).
Both views can be reconciled by saying that *from the point of view of a particular observer* what he's entangled with is a pure product state of the system under observation.

I'm trying to wrap my head around the full implications of this. Does this imply that it is in principle possible to obtain information from one particle about any other particles it has interacted with in the past? Or, put another way, quantum information is never destroyed?

 

[LaserMind]

Actually, the "partial collapse" is demonstrated as true in virtually every Bell test - although that is a by-product rather than a specific element of the Bell test.

It is normal to place filters after the PDC crystal (which is where the input photon is split into 2 output photons). These filters are tuned to a specific frequency of light because it is critical that extraneous light (of which there is a lot coming out of the PDC that is not down-converted) does not go into the detection apparatus. Those filters *absolutely* give us knowledge of wavelength, frequency and energy of the photon that passes - it is an observation! As such, there must be collapse of that part of the wavefunction. Yet... afterwards, we perform a commuting polarization observation on those same photons and notice there is perfect entanglement.

So this is not a speculative issue... partial entanglement is real.

Partial collapse and maintaining entanglement? Then one state could be given a known state preparation that the entangled particle would have 'no idea' about what the value is? How does that work? Have you got a reference for partial collpase re entanglement? Interesting.

 

[peter0302]

Quantum information can absolutely be destroyed. That's exactly what quantum eraser does.

 

[CJames]

maybe I'm not using the right terminology. My point here is that a measurement of one of the entangled particles will give you information about the other particle. In the quantum eraser experiment, I suppose it is true that "which path" information is destroyed for the OBSERVER. What is not destroyed, though, is the fact that IF "which path" information is obtained from one of the particles, the interference pattern collapses. Throughout the entire experiment, each particle contains information about the other.

My question revolves around something more complex. What happens long after the experiment takes place? Vanesch appears to be saying that (for some theoretical observer) the particles will become entangled with the entire experimental setup, and so on inexorably. So the question I'm asking is whether a particle (in principle) contains information about every other particle it has interacted with in the past.

 

[DrChinese]

Partial collapse and maintaining entanglement? Then one state could be given a known state preparation that the entangled particle would have 'no idea' about what the value is? How does that work? Have you got a reference for partial collpase re entanglement? Interesting.

This isn't perfect but it has the filter before the beam splitter:

Multi-photon entanglement

Unfortunately, my usual reference for this type of experiment (Dehlinger and Mitchell) has the filter after the polarizer so the fact that there was partial collapse is not evident.

 

[peter0302]

So the question I'm asking is whether a particle (in principle) contains information about every other particle it has interacted with in the past.

Well, the answer is no, as to "information." It is certainly true that particles are influenced by their entire history, but the extent to which usable information can actually be divined depends on how much the particle has become entangled with the environment.

Imagine tallying up items on a simple calculator. Every time you hit M+, the total updates. The total reflects all of the items that went into it. But that doesn't mean by knowing the total you know the cost of the individual items. Each time you perform a measurement on a particle, it's like hitting M+.

 

[DrChinese]

My question revolves around something more complex. What happens long after the experiment takes place? Vanesch appears to be saying that (for some theoretical observer) the particles will become entangled with the entire experimental setup, and so on inexorably. So the question I'm asking is whether a particle (in principle) contains information about every other particle it has interacted with in the past.

I don't know if I would agree that each particle contains information about all particles it has interacted with in the past. In fact, you would have to say that information is lost at about the same rate it is gained. I think Vanesch is saying that a new system is formed which is itself in a superposition of states. With that many particles, I don't think any individual particle has enough of the story to call it "information". Not sure if that addresses your point or not.

But clearly if the observer had a known net spin state before interacting with another particle with a known spin state, the combined state would be known and presumably would be entangled in a fashion. It breaks my brain to think about. :)

 

[CJames]

Thankyou peter and Dr Chinese. Your answers are very helpful.