Quantum entanglement: where is the pair?

[imsmooth]

I am trying to read some of the experiments on entanglement. Is the pair of photons or electrons created by a laser hitting crystal? If this is so, then a pair of particles emerges? If this is also so, what is the big deal where the measurement occurs? The particles are created together at one location.

If, however, the paired particle is created a distance away, how does one know this particle is matched with the one in the first lab?

Thanks.

 

[Nugatory]

I am trying to read some of the experiments on entanglement. Is the pair of photons or electrons created by a laser hitting crystal? If this is so, then a pair of particles emerges? If this is also so, what is the big deal where the measurement occurs? The particles are created together at one location.

The surprising thing is that, although the two particles were created together at one location, no theory in which the particles acquired their properties (for example, one spin-up and one spin-down) then can explain all correlations between them.

Google for "bell's theorem" and "bertlmann's socks" and also search this forum using those keywords. There's a lot already written here.

 

[DrChinese]

To expand on Nugatory's excellent comment: yes, your conclusion seems correct at first blush. As long as you measure the photons emerging from a PDC crystal at the same angles, it will seem to make good sense and will confirm your basic intuition. This is sometimes referred to as a "Bertlmann's socks" analogy - from John Bell. But Bell had created a theorem (now called Bell's Theorem) which shows how that idea completely breaks down at certain other angle settings. It becomes clear that the observers' choice of angles somehow enters into the equation, in complete violation of the predetermination hypothesis.

 

[imsmooth]

So both photons emerge from the crystal. So how does this affect the situation at another location? The photons get entangled at the same location. I believe I am understanding that the observation of one of the particles from a great distance affects the other, but they are, again, entangled in the same location. Is this correct?

 

[atyy]

So both photons emerge from the crystal. So how does this affect the situation at another location? The photons get entangled at the same location. I believe I am understanding that the observation of one of the particles from a great distance affects the other, but they are, again, entangled in the same location. Is this correct?

Yes, the photons are entangled at the same initial location.

 

[naima]

There is also the entanglement switching.It can entangle photons which did not interact.

 

[vanhees71]

The surprising thing is that, although the two particles were created together at one location, no theory in which the particles acquired their properties (for example, one spin-up and one spin-down) then can explain all correlations between them.

Google for "bell's theorem" and "bertlmann's socks" and also search this forum using those keywords. There's a lot already written here.

No! The point is Quantum Theory predicts these strong correlations, and all very accurate measurements testing these predictions turn out to be correct with an amazing significance. Put it in another way: QT is the only theory that can explain the observed facts about entanglement.

Also the OP is right with his idea that there is nothing surprising, given quantum theory and the probabilistic meaning of states, and the fact that the entangled photons/particles have been created together, before any measurements take place. Of course, there are problems with causality as soon as one uses a "collapse of the state" in ones interpretation of QT. As long as you stick to the facts, i.e., the minimal statistical interpretation, no such troubles occur, and QT is a very consistent and utmost successful description of nature!

 

[Nugatory]

No! The point is Quantum Theory predicts these strong correlations, and all very accurate measurements testing these predictions turn out to be correct with an amazing significance. Put it in another way: QT is the only theory that can explain the observed facts about entanglement.

Indeed it is. I interpreted the original question as "Bertlmann's socks aren't surprising, and I don't see why they shouldn't be an adequate model for the observed facts about entanglement", and there is a surprise in store if that's the starting point.

I agree with you about the MSI (for me, it's the only way of making sense of spacelike-separated measurements of an entangled quantum system).

 

[vanhees71]

Ah, I see. I didn't get the Bertlmann's socks thing. I guess, I've finally to read more about Bell's funny metaphors or perhaps even his original papers in more detail. I've only read about the Bell inequality in textbooks so far. It's a good idea, because it's 50 years ago when his groundbreaking ideas emerged :-). Indeed, I've also never seen another interpretation which makes sense concerning the spacelike-separated measurements of entangled states, proving the corresponding correlations of totally indetermined observables (e.g., polarization of the single photons in an entangled pair of photons created in parametric down conversion in the Aspect-Zeilinger like experiments).

 

[DrChinese]

So both photons emerge from the crystal. So how does this affect the situation at another location? The photons get entangled at the same location. I believe I am understanding that the observation of one of the particles from a great distance affects the other, but they are, again, entangled in the same location. Is this correct?

They start out at the same location, but are quickly routed away from each other before they are measured. They remain entangled all of that time. This is what makes the situation confusing, because they do not appear to operate as independent entities. The act as a system of 2 particles, despite the distance separating them. There is a mutual dependency. Please keep in mind that no one knows how this happens.

The important thing is that the statistical correlations at specific angles varies from what might be logically expected based on your hypothesis - which for Type I entanglement cannot be less than 33% agreement at 120 degree separation. Measuring entangled photons at 120 degree separation yields a value of 25% which matches the quantum prediction. So the hypothesis fails. To see WHY the math yields the 33% for your hypothesis requires a familiarity with the ideas of Bell's Theorem.

 

[RonL]

I am trying to read some of the experiments on entanglement. Is the pair of photons or electrons created by a laser hitting crystal? If this is so, then a pair of particles emerges? If this is also so, what is the big deal where the measurement occurs? The particles are created together at one location.

If, however, the paired particle is created a distance away, how does one know this particle is matched with the one in the first lab?

Thanks.

I'm a complete novice about these things, have never been able to quite see the splitting and entanglement until DrChinese posted this link on another thread.

http://arxiv.org/ftp/quant-ph/papers/0607/0607182.pdf

Page 6, fig.1 shows the complete setup between two islands, the mechanics of the equipment, this single picture made it clear to me how everything is done.
If you haven't seen this I hope it will help, and thanks go to DrChinese from me.:)

 

[imsmooth]

They start out at the same location, but are quickly routed away from each other before they are measured. They remain entangled all of that time.

I've started to read your link, which so far is very helpful. I have more to go. However, if the particles are entangled such that one is up and one is down, what is the big deal? If I measure particle one to be up then particle two is down at another location. Is it that I can force particle one to a particular state and this then affects particle two?

 

[atyy]

I've started to read your link, which so far is very helpful. I have more to go. However, if the particles are entangled such that one is up and one is down, what is the big deal? If I measure particle one to be up then particle two is down at another location. Is it that I can force particle one to a particular state and this then affects particle two?

Classically, one can prepare the correlations at the source (eg. spins always anti-parallel), so that measuring one immediately tells you about the other. However, quantum mechanics allows you to prepare them in a superposition of an up-down pair and a down-up pair. This is entanglement, and the degree of nonlocal correlation that can be produced exceeds what can be produced by any classical correlations at the source.

 

[DrChinese]

I've started to read your link, which so far is very helpful. I have more to go. However, if the particles are entangled such that one is up and one is down, what is the big deal? If I measure particle one to be up then particle two is down at another location. Is it that I can force particle one to a particular state and this then affects particle two?

It seems that way, and no experiment contradicts this conclusion. As I say, no one actually knows for sure.

1. Imagine that Alice measures at 0 degrees. We now know what Bob will see at 0 degrees. If Alice measures at 10 degrees, we know then what Bob will see at 10 degrees. If Alice measures at 20 degrees, we know then what Bob will see at 20 degrees. And so on for all possible angles. If polarization is determined at creation, then all of these observational values are predetermined, correct?

2. Imagine that Alice measures at 0 degrees. We now know what Bob will see at 0 degrees. But what if Bob measures at 120 degrees? Or 240 degrees? The ratio of 0/120, 120/240 and 0/240 degrees must be equal if there is no preferred direction. Agree?

3. The observed value of observation angle pairs 0/120, 120/240 and 0/240 are in fact equal, and the value is 25%

4. 1, 2 and 3 above are incompatible. That is what Bell proved. You can try it for yourself and see the problem, you only need about 10 samples to get an obvious difference with experiment.

 

[vanhees71]

They start out at the same location, but are quickly routed away from each other before they are measured. They remain entangled all of that time. This is what makes the situation confusing, because they do not appear to operate as independent entities. The act as a system of 2 particles, despite the distance separating them. There is a mutual dependency. Please keep in mind that no one knows how this happens.

That's the point: The remain entangled. There's no more you need to say. It's not clear to me, what you mean by "mutual dependency". This might be misunderstood as if there is a kind of interaction involved, which is not the case. Photons are (asympotically) free states. So the photons do not interact anymore (in the idealized picture, which however works very well).

The two-photon state is
$$|\Psi \rangle=\frac{1}{2} (|u_1,u_2 \rangle - |u_2,u_1 \rangle ) \otimes (|HV \rangle-|VH \rangle),$$
where I wrote the "wave packets" as a tensor product of the spatial and the polarization part. Together it's a state symmetric under exchange of the two photons as it must be, because they are bosons. The spatial parts $|u_j \rangle$ are wave packets (or rather long wave trains, because the momentum of the photons is quite well defined, but in any case real Hilbert-space states, normalizable to 1) with a momentum (wave-number) direction pointing back to back. To get the probabilities you have to put projectors for the polarization filters and an appropriate spatially located state, describing your photo detector (e.g., a CCD camera). There's nothing more to it. I don't know, how to describe this pretty straight-forward math in words, because I can't use everyday language to describe quantum correlations, encoded in such entangled states, but the math is much more accurate in any case anyway :-).

 

[DrChinese]

It's not clear to me, what you mean by "mutual dependency". This might be misunderstood as if there is a kind of interaction involved, which is not the case.

By mutual I mean: neither is in a preferred position in the sense that an observation on Alice does not affect Bob any more than vice versa; with the added comment that this is not resolved by considering ordering of measurements.

As to the interaction part: certainly you can add the words "as if there is an interaction" but I have no idea if there is an interaction or not. What is collapse? Is it physical? This is really interpretation dependent. But if you are starting from the OP's perspective, you are trying to explain a quantum effect using "common sense". Obviously, not likely to be so successful.

 

[vanhees71]

According to relativistic quantum field theory there is no action at a distance but only interactions local in space and time (at least for the so far developed successful local relativistic QFTs, underlying the Standard Model). When Alices measures the polarization of her photon, this occurs by local interactions of her photon with the measurement devices used at her place. By the way, you can associate a position only to this measurement act; the photon itself has no position observable in the strict sense at all. You only can give a probability for detecting a photon at a given place (due to the preparation of the entangled pair, in the sense I've described in my previous posting).

The collapse is not a physical process within the minimal interpretation. It's just the adaption of our knowledge to measurements on the system. It's not much different from looking at the outcome of any other random experiment. When playing dice and you read the outcome, you also have no problem saying that now a certain outcome has occurred in a single experiment.

For me there is no principle difference between the probabilities concerning a classical random experiment or a quantum measurement. The only difference is that quantum theory admits entanglement and much stronger correlations between spatially separated parts of a quantum system than possible within classical local theories.

 

[Jilang]

I am struggling with this very concept at the moment. The whole crux of the matter seems to be that the effect on a particle by a measurement at A is independent of the effect on a particle of a a measurement at position B. The bit that concerns me is that if both effects are dependent on a third variable pertaining to the particle, can the effects at A and B be said to be independent?

 

[atyy]

I am struggling with this very concept at the moment. The whole crux of the matter seems to be that the effect on a particle by a measurement at A is independent of the effect on a particle of a a measurement at position B. The bit that concerns me is that if both effects are dependent on a third variable pertaining to the particle, can the effects at A and B be said to be independent?

Bell showed that quantum mechanics is inconsistent with local causality: no classical relativistic dynamics can explain the nonocal quantum correlations. But local causality itself can be derived from relativistic causality and the principle of common cause. Does quantum mechanics give up relativistic causality or the principle of common cause? There is an extremely interesting discussion of the issue by Cavalcanti and Lal in http://arxiv.org/abs/1311.6852.

 

[Jilang]

Thanks, this does allude to the "separability of probabilities" which is the source of my worries. I can reconcile this with the measurement (or repeated measurement) of a single pair of particles,but doesn't it hit a clean dead wall when trying to apply the idea to a number of pairs of particles?

 

[atyy]

Thanks, this does allude to the "separability of probabilities" which is the source of my worries. I can reconcile this with the measurement (or repeated measurement) of a single pair of particles,but doesn't it hit a clean dead wall when trying to apply the idea to a number of pairs of particles?

Everyone agrees that there is no separation of probabilities. The probability of an outcome at one location is not independent of the measurement choice and outcome at a distant location. This indicates that no classical relativistic dynamics can explain quantum mechanics. However, a notion of locality is retained, because the probability of an outcome at one location is independent of the measurement choice at a distant location. This indicates that quantum mechanics is consistent with the relativistic requirement of no superluminal communication of classical information. Beyond that, it is a matter of interpretation, and you can use any interpretation you find helpful.

 

[morrobay]

According to relativistic quantum field theory there is no action at a distance but only interactions local in space and time (at least for the so far developed successful local relativistic QFTs, underlying the Standard Model). When Alices measures the polarization of her photon, this occurs by local interactions of her photon with the measurement devices used at her place. By the way, you can associate a position only to this measurement act; the photon itself has no position observable in the strict sense at all. You only can give a probability for detecting a photon at a given place (due to the preparation of the entangled pair, in the sense I've described in my previous posting).

The collapse is not a physical process within the minimal interpretation. It's just the adaption of our knowledge to measurements on the system. It's not much different from looking at the outcome of any other random experiment. When playing dice and you read the outcome, you also have no problem saying that now a certain outcome has occurred in a single experiment.

For me there is no principle difference between the probabilities concerning a classical random experiment or a quantum measurement. The only difference is that quantum theory admits entanglement and much stronger correlations between spatially separated parts of a quantum system than possible within classical local theories.

If algebraic relativistic quantum field theory is stochastic and Einstein local. Could you explain/elaborate how this theory accounts for the unequal distributions in Bell inequality violations ? I realize that ARQFT is complex but there is such an information overload on Bell's theorem
explanations are appreciated. For example in this paper http://dare.uva.nl/document/2/104604 the author concludes that Bell assumed a not necessarily satisfied mathematical condition, devoid of relevant physical mechanisms.

 

[vanhees71]

If algebraic relativistic quantum field theory is stochastic and Einstein local. Could you explain/elaborate how this theory accounts for the unequal distributions in Bell inequality violations ? I realize that ARQFT is complex but there is such an information overload on Bell's theorem
explanations are appreciated. For example in this paper http://dare.uva.nl/document/2/104604 the author concludes that Bell assumed a not necessarily satisfied mathematical condition, devoid of relevant physical mechanisms.

I'm not an expert in algebraic QFT but only a practitioner of QFT.

What's ment with "locality" is that the (a) Lagrangian (and thus also the Hamiltonian) of the system is built by polynomials of field operators at one space-time point which (b) transform locally under proper orthochronous Lorentz transformations, which fulfill the constraints of microcausality (local observables commute at space-like distances) and boundedness of the Hamiltonian, which leaves massive and massless fields for interacting field theories and exclude tachyonic representations of the Poincare group.

The so constructed QFTs have a unitary and Poincare invariant S matrix (at least in the perturbative sense) and fulfill the linked-cluster principle. The latter means that space-like well-separated experiments have stochastically independent outcomes. This implies that there cannot be any faster-than-light signal propagations within these theories.

This, of course, does not exclude the very strong correlations between spacelike separated (sub-)systems, described by entanglement, but this does not contradict the linked-cluster principle of course. In an experiment like the Aspect-Zeilinger experiment with polarizations of photons the correlations can only be empirically checked by performing experiments on (large) ensembles of independently prepared entangled photon pairs and can only be revealed by comparing "Alice's" and "Bob's" measurement protocols via a classical channel after both have measured their photons. So there is no faster-than-light signal transmission at all. This comes only into the game, when one introduces "collapse postulate" in the sense that the quantum state instantaneously changes the state to an eigenstate of the measured observable with the corresponding value revealed by the measurement. This is a contradiction to Einstein causality but, in my opinion, a completely useless and unnecessary additional metaphysical hypothesis on top of the scientific part of the interpretation necessary to relate the mathematical formalism of quantum theory to experiment with real objects, for which the minimal interpretation is fully sufficient.

The paper by Nieuwenhuizen linked in your posting, I've to first read carefully (and understand it, which is the difficult part here :-)).

 

[atyy]

This, of course, does not exclude the very strong correlations between spacelike separated (sub-)systems, described by entanglement, but this does not contradict the linked-cluster principle of course. In an experiment like the Aspect-Zeilinger experiment with polarizations of photons the correlations can only be empirically checked by performing experiments on (large) ensembles of independently prepared entangled photon pairs and can only be revealed by comparing "Alice's" and "Bob's" measurement protocols via a classical channel after both have measured their photons. So there is no faster-than-light signal transmission at all. This comes only into the game, when one introduces "collapse postulate" in the sense that the quantum state instantaneously changes the state to an eigenstate of the measured observable with the corresponding value revealed by the measurement. This is a contradiction to Einstein causality but, in my opinion, a completely useless and unnecessary additional metaphysical hypothesis on top of the scientific part of the interpretation necessary to relate the mathematical formalism of quantum theory to experiment with real objects, for which the minimal interpretation is fully sufficient.

But why single out collapse? In a minimalistic interpretation wouldn't the wave function itself be not necessarily real, and just a tool? Only measurement outcomes are real, because they are classical relativistically invariant events. Once we agree that everything about the wave function is not necessarily real, and just FAPP real for a given choice of system, apparatus, reference frame and Hilbert space, then wouldn't the wave function, unitary evolution and collapse be equally real or unreal?

The paper by Nieuwenhuizen linked in your posting, I've to first read carefully (and understand it, which is the difficult part here :) ).

In talking about the Bell inequalities, we say that they show that quantum mechanics is not Bell local. We are talking about predictions of a theory, so we can assume that different runs of the experiement are iid samples. However, Nieuwenhuizen is talking about real experiments, and the possibility that nature (not quantum mechanics) is local, because the iid assumption is not satisfied. For example, could local realism be preserved if the measurement choice and outcome on one run affect the preparation on the next run? This is also called the memory loophole. For any finite number of trials, even given the iid assumption, Bell nonlocality of course cannot be proven, just made unlikely. It is true that for the same number of finite trials, if the iid assumption is not taken, and the memory loophole allowed, then Bell nonlocality becomes less likely, ie. the probability that the data can be generated by local realism increases. This issue is discussed in:
http://arxiv.org/abs/quant-ph/0110137
http://arxiv.org/abs/quant-ph/0301059
http://arxiv.org/abs/quant-ph/0205016
http://arxiv.org/abs/1108.2468

 

[vanhees71]

But why single out collapse? In a minimalistic interpretation wouldn't the wave function itself be not necessarily real, and just a tool? Only measurement outcomes are real, because they are classical relativistically invariant events. Once we agree that everything about the wave function is not necessarily real, and just FAPP real for a given choice of system, apparatus, reference frame and Hilbert space, then wouldn't the wave function, unitary evolution and collapse be equally real or unreal?

That's exactly the point! There's no collapse in the minimal interpretation, and the quantum state is just a description of our (probabilistic!) knowledge about the system due to an equivalence class of prepartion procedures. This is the operational definition of what a quantum state is, which in the formalism is represented by the Statistical operator.

Concerning the tests of the Bell inequality and related theorems and the various loopholes and the current status of their experimental resolution: is there a good recent review article on this topic, so that I can get an overview first?

 

[atyy]

That's exactly the point! There's no collapse in the minimal interpretation, and the quantum state is just a description of our (probabilistic!) knowledge about the system due to an equivalence class of prepartion procedures. This is the operational definition of what a quantum state is, which in the formalism is represented by the Statistical operator.

I think we agree since we both seem to like Landau and Lifshitz. :) I guess whenever you say "collapse" you mean "physical collapse", whereas I always mean "FAPP" unless I'm not talking about quantum mechanics, but something beyond the standard theory like GRW or CSL.

Concerning the tests of the Bell inequality and related theorems and the various loopholes and the current status of their experimental resolution: is there a good recent review article on this topic, so that I can get an overview first?

Maybe section VII.B and VII.C of the huge review by Brunner et al http://arxiv.org/abs/1303.2849. The contextuality or memory loophole is discussed in VII.B.3 under finite statistics (the Nieuwenhuizen paper is not mentioned, but the issue is).