# Quantum entanglement: where is the pair?

1. Nov 26, 2014

### 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.

2. Nov 26, 2014

### Staff: Mentor

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.

Last edited: Nov 27, 2014
3. Nov 26, 2014

### 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.

4. Nov 26, 2014

### 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?

5. Nov 26, 2014

### atyy

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

6. Nov 27, 2014

### naima

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

7. Nov 27, 2014

### vanhees71

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!

8. Nov 27, 2014

### Staff: Mentor

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).

9. Nov 27, 2014

### 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).

10. Nov 27, 2014

### DrChinese

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.

11. Nov 27, 2014

### RonL

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.:)

12. Nov 27, 2014

### imsmooth

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?

13. Nov 27, 2014

### atyy

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.

14. Nov 27, 2014

### DrChinese

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.

15. Nov 28, 2014

### vanhees71

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 :-).

16. Nov 28, 2014

### DrChinese

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.

17. Nov 28, 2014

### 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.

18. Nov 28, 2014

### 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?

19. Nov 28, 2014

### atyy

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.

20. Nov 28, 2014

### 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?