Undergrad Entanglement in QM - Understanding Instant Correlation & Randomness

[rubi]

As to the "textbook" definition of entanglement, I fail to see how the system of photons 1&4 are in a product state. Obviously they share a state.

So if you fail to see how photons 1&4 are in a product state, then you should agree that their state doesn't meet the textbook definition of an entangled state, so they aren't entangled by the standard definition.

So I guess that is where we leave it.

The problem is that you misunderstand everything I write:

I stand by the characterization of photons 1&4 being entangled (the title is after all "Entanglement Between Photons that have Never Coexisted"). Such entanglement is both non-local ("the nonlocality is confirmed by observing a violation of Bell's inequality by 4.5 standard deviations. ") and non-temporal ("the observed quantum correlations manifest the non-locality of quantum mechanics in spacetime") exactly as claimed in the cited articles.

The authors use a non-textbook definition of entanglement. What they mean is just that their experiment reproduces the statistics of entangled particles. I never denied that the correlations in their experiment are non-local and non-temporal. However, this is completely unproblematic in a local theory. The correlations in my above example are also non-local and non-temporal, even though classical Maxwell electrodynamics is a perfectly local theory. There is no contradiction between your claim and my claim.

Obviously at some level, the descriptions used by Zeilinger et al do not match yours. You have yet to present any reference to support your position other than to agree with the articles but disagree with me - which seems odd.

I have told you that my definition of entanglement agrees with the textbook definition. I thought it was enough to point you to the textbooks, but if you want a specific one, you can check out "Quantum Theory, Concepts and Methods" by Peres.

Any 2 particles (or a stream of same) that exhibit perfect spin correlations at any angle are entangled.

This does not apply to your photons 1 and 4. Photons 1 and 4 show absolutely no correlation at any angle. In order to get the correlations, you need to select a subsequence of events based on measurements of photons 2 and 4, so you need data from overlapping spacetime regions. You seem to ignore this point entirely, so it doesn't make sense to continue the discussion, since this is my main point. The subset of events that show quantum correlations must be collected from data from overlapping spacetime regions, otherwise you will see no correlation.

By the way, I'm not saying anything that can't be found in textbooks. In fact, I'm defending the mainstream position.

 

[PeterDonis]

So if you fail to see how photons 1&4 are in a product state, then you should agree that their state doesn't meet the textbook definition of an entangled state, so they aren't entangled by the standard definition.

I'm confused. Isn't the textbook definition of entanglement that the state can't be written as a product state (but only as the sum of multiple product states)? So if photons 1 and 4 are not in a product state, doesn't that mean they do meet the textbook definition of an entangled state?

 

[DrChinese]

The authors use a non-textbook definition of entanglement.

As I said, you are rejecting the work of some of the top physicists in the field. And it is a bit lame to reference an entire textbook in support of your position. If there is something specific being referenced in support of a position, the norm is to cite that as I have. On the other hand, since you cited the book by Peres written in 1995, I wonder what he had to say in 2000 relevant to the experiment I cited by Zeilinger et al. Hmmm, perhaps you would look at page 5 of that.

"As shown in Fig. 3, the observed fidelity of the entanglement of photon [1] and photon [4] matches the fidelity in the non-delayed case within experimental errors. Therefore, this result indicate that the time ordering of the detection events has no influence on the results and strengthens the argument of A. Peres [4, published in 2000]: this paradox does not arise if the correctness of quantum mechanics is firmly believed."

The reason that the entangled state stats are reproduced in the cited papers is that the photons (1&4) are entangled. In fact, you could set it up so you could predict with certainty the outcome of each and every photon 4 polarization outcome, for example, and they (1&4) still will never have interacted in the past nor existed in a common light cone. And in conjunction with the OP question: it will not be possible to identify the point in time they became entangled, nor precisely at which point they ceased to be entangled. And yet all of this is standard QM.

So if you want to cling to your textbook definition of entanglement, I will simply say that it is outdated - and the author of your citation has agreed in a subsequent paper referenced by Zeilinger et al. Seriously, the state of the art on these experiments has moved a long way in the past 5, 10, 20 years. Entanglement comes in many exotic forms, and traditional notions of locality and causality - such as you may adhere to - do not serve to adequately describe what is going on. You can entangle particles that have never interacted after detection, before detection, within a common light cone, or fully non-locally. For another example of the technique I have cited (swapping), check out this important 2015 result:

https://arxiv.org/abs/1508.05949
"We employ an event-ready scheme that enables the generation of high-fidelity entanglement between distant electron spins. ... Our experiment realizes the first Bell test that simultaneously addresses both the detection loophole and the locality loophole." Photons [2&3] are used as critical components for the entanglement of the electrons, which serve in the same role as photons 1&4 in my examples.

 

[rubi]

I'm confused. Isn't the textbook definition of entanglement that the state can't be written as a product state (but only as the sum of multiple product states)? So if photons 1 and 4 are not in a product state, doesn't that mean they do meet the textbook definition of an entangled state?

For entanglement, you need a tensor product of individual system and a state that can't be written as a tensor product within this space. However, that doesn't apply in this case, since at no point in time (for any observer), the two photons 1 and 4 exist simultaneously. If we want to put in mathematically, we have to describe this experiment in a Fock space. The states of the system during its time evolution are (very roughly, up to phases and normalization and we really need density matrices):

1. $\psi_1\otimes\psi_2 + \psi_2\otimes\psi_1$
2. $\psi_2$
3. $\psi_2\otimes(\psi_3\otimes\psi_4+\psi_4\otimes\psi_3)$
4. $\psi_4$

But at no time, for no observer, the system is in a state $(\psi_1\otimes\psi_4+\psi_4\otimes\psi_1)\otimes\psi_{\text{something else}}$, since at no time, photons 1 and 4 coexist.
After post-selection, we will find statistics that matches the statistics of a hypothetical state $\psi_1\otimes\psi_4+\psi_4\otimes\psi_1$ for coexisting photons 1 and 4. However, it's only the statistics that matches this state. The system itself is never in this state.

 

[DrChinese]

I'm confused. Isn't the textbook definition of entanglement that the state can't be written as a product state (but only as the sum of multiple product states)? So if photons 1 and 4 are not in a product state, doesn't that mean they do meet the textbook definition of an entangled state?

 

[rubi]

As I said, you are rejecting the work of some of the top physicists in the field. And it is a bit lame to reference an entire textbook in support of your position.

What is really lame is that you pretend I would reject the work of any physicist. I really have said multiple times that I am not rejecting anything written in these papers. What I am rejecting is your personal interpretation of what these papers imply. If you want to discuss this, then please stop pretending that I would reject the papers. I am in 100% agreement with these papers.

It seems like I can't get my point across and you never address the actual argument. So let me ask you a few simple yes/no questions:
1. Do you agree that the statistics in this experiment is collected from overlapping spacetime regions?
2. Do you agree that my example in post #23 features non-local and non-temporal correlations of light pulses that have never coexisted?
3. Do you believe that my example in post #23 shows that classical Maxwell electrodynamics is non-local?

 

[DrChinese]

However, it's only the statistics that matches this state. The system itself is never in this state.

This conclusion is ridiculous on the face of it, and is actually a denial (although it may not be obvious) of Bell's Theorem. The issue here is your use of the word "never". The system was in the entangled state, but "never" at a single point in time. So what?

My entire point triggering this discussion is that an entangled system can consist of particles that have never co-existed. I have produced citation after citation on this point, and can provide more. If they "never" co-existed, you define them to not be entangled. So you are assuming that which you seek to prove. That's wrong and obviously outdated, as I mention in my post #33 above.

 

[PeterDonis]

After post-selection, we will find statistics that matches the statistics of a hypothetical state $\psi_1\otimes\psi_4+\psi_4\otimes\psi_1$ for coexisting photons 1 and 4. However, it's only the statistics that matches this state. The system itself is never in this state.

You appear to be using a non-relativistic framework, where we can meaningfully speak of the "state" of a spatially extended system at a particular "time". I'm not sure the papers in question are actually using such a framework, given that the authors appear to be adopting the very interpretation you are rejecting.

What I am rejecting is your personal interpretation of what these papers imply.

As I read the papers, it also appears to be the interpretation of the authors. That in itself doesn't necessarily make it correct, but it does mean it isn't just DrChinese who is adopting this interpretation.

 

[PeterDonis]

Thread closed for moderation.

[Edit: The thread will remain closed.]