# I Entanglement in QM

1. Nov 15, 2016

### GiuseppeP

Hello,

I have red on the web about the entanglement, but there is one thing that it is not clear to me: to explain it, why we cannot just say that randomness and correlation between the two entangled particles is happening at instant of their creation and from that time on they stay in that condition until the entanglement is broken?

Thank you.

2. Nov 15, 2016

### zonde

3. Nov 15, 2016

### DrChinese

As zonde mentions: Your assumption leads to a contradiction with observed results and QM's predictions (which match observations). This was discovered by Bell (1964) and is expressed by Bell's Theorem. The short version is that entangled pairs are correlated at many angles in a fashion that no predetermined data set could support.

The only meaningful loophole is that there is faster than light communication between members of the pair. The result is that you either deny the existence of predetermined values at all possible measurement setting (there are no hidden variables); or you deny that the speed of light c is the limit for causal influences. Your choice between these 2 options...

4. Nov 15, 2016

### Jilang

Would it preclude the possibility of one real and one random variable also?

5. Nov 17, 2016

### jk22

What do you mean by real variable and random variable ?

Anyhow Bell's theorem has nothing against global variable in the sense $$AB (a,b,\lambda)$$

There is an argument by https://arxiv.org/abs/quant-ph/0006014 saying the Chsh operator should contain a different variable for each pair ie $$A (a,l1)B (b,l1)-A (a,l2)B (b,l2)...$$

But if you think this argument comes back to admit the pairs are independent. Calculation of the probabilities with the local model gives but the same as bell's result the difference is that there is a variance namely $$|<Chsh>|_{lhv}=2\pm \sqrt {3}/2$$

Whereas $$|<Chsh>|_{qm}=2\sqrt {2}\pm 1/\sqrt {2}$$

6. Nov 17, 2016

### Jilang

I am thinking of a fixed flagpole with a spinning flag, where for entangled pairs the flagpoles are in opposite directions and the spinning direction is opposite for each. The fixed flagpole is the real variable, the spinning flag direction wrt the pole, the variable one.

7. Nov 17, 2016

### jk22

This is exactly the local model used which is A=sgn (a.l) : the result is the signum of the projection of the flag on the measurement direction.

This function howere has nothing 'transcendent' since one would imagine very quick varying one in the neighborhood of one given lambda

8. Nov 17, 2016

### DrChinese

Jilang, certainly by now you know that model wouldn't work to enable agreement with observation.

9. Nov 17, 2016

### Jilang

That's what's bothering me. It might be "quick-varying"' but will still hit the plane of observation from a given direction.

10. Nov 17, 2016

### Jilang

No, I have only seen proofs that rule out predetermined existing variables. I am struggling to see though how a composite of one real and one random variable wouldn't work.

11. Nov 17, 2016

### DrChinese

Either: a) there is no difference between predetermined and "random" variables functionally, in which case the outcome is the same as Bell; or b) the random variable acquires its value independently at a later time. If so, and the random variable is local, then you cannot reproduce perfect correlations. So you are back to where you started.

12. Nov 18, 2016

### vanhees71

As is well-known in this forum I disagree, and I'd answer the question in #1 in the positive. The entangled state is created in the very beginning and stays an entangled state as long as there's no disturbance that changes it to a "disentangled" state.

To be specific, let's take the standard experiment with a pair of polarization-entangled photons. They are created by interaction of a laser field with a birefringent crystal by a process called parametric down conversion. Then the corresponding two-photon state, with a polarization part given by
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle-|VH \rangle).$$
The single photons have maximally uncertain polarization, i.e.,
$$\hat{\rho}_A=\mathrm{Tr}_B |\Psi \rangle \langle \Psi|=\frac{1}{2} \hat{1}=\hat{\rho}_B,$$
i.e., A and B measure just perfectly unpolarized photons. Nevertheless there is a 100% correlation between measurements, i.e., whenever A measures her photon to be H polarized Bob necessarily finds his photon V polarized and vice versa.

The correlation described by the entanglement is there for the whole time, from the creation of the two photons until to their detection much later. There is for sure no faster-than-light interaction triggered by A's measurement with B's photon and vice versa since this is ruled out by the very construction of QED as a local microcausal relativistic QFT. There are very long threads about this in this forum, and we don't need to repeat all the arguments against this view, but for me this is still the only view that is consistent with both the theoretical foundations of QED and observations.

13. Nov 18, 2016

### Staff: Mentor

We can; in fact that's what we do say. What we don't say is that "correlation between two entangled particles" means that the results of all possible measurements that could be made on them are determined at the instant of their creation. That sort of model is ruled out by experiment, as zonde and DrChinese have pointed out. But, as vanhees71 has pointed out, that does not mean the entanglement itself is ruled out; it isn't. You just have to be clear on what entanglement means.

I don't think the OP was necessarily assuming that "entanglement" means "predetermined data set".

So would I, because I don't think that the OP necessarily had in mind a local hidden variable model to begin with.

14. Nov 18, 2016

### DrChinese

You and vanhees71 probably read that as he meant it. I just assumed he was referencing some form of a hidden variable model. My bad.

The effect we call "entanglement" does not have a clear, well-defined start and end point. In the OP's example, there looks to be a simple explanation of the starting point for the entanglement - it's when the particle pair is created. (Not so clear when the end point occurs though.) On the other hand, there are entanglement examples (swapping comes to mind) where the start point of entanglement is not so well defined. You can have entangled particles that have never co-existed. To me (and not everyone would agree), that shows how difficult it is to reduce such effects to everyday language.

15. Nov 18, 2016

### vanhees71

Well, for entanglement swapping you need entangled systems, you have prepared as such. I've no example, where some entangled system is not somehow prepared with some local process, i.e., where there's no causal connection between the entangled parts of a system in the past.

16. Nov 18, 2016

### jk22

Note that if you accept supraluminal influences then information has to be sent from one to the other and that not only the result has to but the measurement configuration too which makes this solution to seem quite improbable since the variable would have to carry a huge information like a real number and not only a bit.

Functionally B (A(a,l),b) is not sufficient but it has to be B (A (a,l),a,b) which makes a slight difference.

17. Nov 18, 2016

### DrChinese

To entangle particles A & D, there must be "something" they must have interacted with in some common past individually. But A & D never need to have co-existed in a common light cone; so they have never interacted with each other, nor has there been any possible signal between them intermediated by that "something". The decision to entangle A & D can occur after they no longer exist.

So this blurs the idea that entanglement begins at point T1 and ends at point T2.

18. Nov 19, 2016

### vanhees71

Give an example with a complete preparation/measurement procedure, where this is done. Maybe then I can point out on this example what I mean.

19. Nov 19, 2016

### jk22

Is this similar to the before before experiment where Suarez deduced that the correlation comes from 'outside' spacetime ?

20. Nov 19, 2016

### DrChinese

This is the effect I am referring to. A-D in my example correspond to their photons 1-4. When does the entanglement between photons 1&4 start, and when does it end? Certainly you can define it however you like, but no answer is very convincing.
https://arxiv.org/abs/1209.4191
Entanglement between photons that have never co-existed.
The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime.