Can you determine if a string of particle pairs is composed of entangled pairs?

[MartijnWetering]

I've gotten interested in this question since the recent loophole free bell test performed at Delft University (group of Ronald Hanson). In this test they use entanglement swapping which I hadn't heard about before.

After some research I even found out that there is such a thing as delayed choice entanglement swapping. http://www.nature.com/nphys/journal/v8/n6/full/nphys2294.html

After reading that article I got a similar epiphany of FTL and back in time communication as the writer, matrixising, of this post
https://www.physicsforums.com/threads/entanglement-swapping-and-ftl-communication.731061/

This thread ended into some bad communication. The key point of discussion was how the observers Alice and Bob can determine whether their electrons or photons 1 & 4 are entangled or not. Some people communicated that this was not possible since the measurements of the correlations will be similarly random for entangled and non-entangled particle pairs.

My question in this matter is what about bell's inequality? Given a set of pairs of particles, isn't there a difference between their correlations (namely violation of the inequality), based on whether the pairs are entangled or not? Isn't this a method to determine entanglement? And isn't this what the article by Xiao-song Ma shows in Figure 3 (While entangled states can show maximalcorrelations in all three bases (the magnitude of all correlation functions equals 1 ideally), separable states can be maximally correlated (ideal correlation function 1) only in one basis, the others being 0)?

 

[Strilanc]

Suppose Alice shares many EPR pairs with Eve, and Bob shares many EPR pairs with Eve, and Eve may or may not perform entanglement swapping. (The pairs are numbered, so Alice and Bob know Alice's qubit #3 is only ever paired (or not) with Bob's qubit #3 and etc.)

Eve decides to perform the entanglement swapping on all the pairs.

Alice and Bob run entanglement-detecting bell tests on the pairs of qubits they know might be entangled.

And... the tests fail. They detect no entanglement!

You were expecting them to pass the test, right? That's not what happens.

The problem is that there are multiple different types of entanglement in play, they all pass the bell test in different ways, and those differences cancel each other out in aggregate. When Eve performs the entanglement swapping, she does some measurements. The results of those measurements indicate what type of entanglement was created. That information needs to be communicated to Alice and Bob, so they can group their bell tests based on entanglement type (or correct all the entanglement types to the same type).

Alice and Bob need to filter their results based on Eve's measurement results. Only then will they be able to detect that any entanglement was present. Getting those measurement results from Eve to Alice/Bob requires good old fashioned non-FTL communication, and is not instantaneous.

 

[MartijnWetering]

Thank you Strilanc.

I was close to tracking the errors in my train of thought. I am getting better now what the missing puzzle piece is.

regarding the articles:

- The statistics generated in the article by Xiao-song Ma is based on a subsets of the pairs. They either have a Φ⁺ or Φ⁺ state after entanglement swapping. Their presented results of the correlations are only for a subset of pairs that belongs to one of these states.
- In the Delft experiment they use a phrase like "For each trial, the two spins are prepared into the entangled state Ψ^-" (from which my confusion originated). But this is not what they actually do (as in physically choosing/selecting that specific state). They entangle the electrons by a Bell measurement of the photons, which simultaneously determines whether the electrons are in the Ψ^- state. It is not that this state is the only entangled state that they create with this scheme. ("If...the observation of...the spins at A and B into the maximally entangled state Ψ^-").

 

[Strilanc]

Incidentally, if you want a clear explanation of what they did in the loop-hole-free bell test, Scott Aaronson has a good blog post about it.