I recently read an article about \"Delayed-choice entanglement swapping\". Here
ID: 1375481 • Letter: I
Question
I recently read an article about "Delayed-choice entanglement swapping". Here is an excerpt from the article:
Delayed-choice entanglement swapping consists of the following steps. (I use the same names for the fictional experimenters as in the paper for convenience, but note that they represent acts of measurement, not literal people.)
Two independent sources (labeled I and II) produce pairs photons such that their polarization states are entangled. One photon from I goes to Alice, while one photon from II is sent to Bob. The second photon from each source goes to Victor. (I'm not sure why the third party is named "Victor".)
Alice and Bob independently perform polarization measurements; no communication passes between them during the experiment
Explanation / Answer
Please believe me that if the experiment were done not with two pairs of entangled photons, but with two pairs of entangled electrons, the results were similar, except that the wave-function of two entangled fermions is antisymmetrical instead of symmetrical. So, the light velocity plays no role here.
I recommend you look at the equation (2) in the article "Experimental delayed-choice entanglement swapping" in quant-ph/1203.4834,
arxiv.org/ftp/arxiv/papers/1203/1203.4834.pdf.
You see in this formula first of all that the polarization state of two photons can be expressed in the Bell-base, which contains four vectors, |?+?, |?-?, |?+?, and |?-?. Now, since we have two pairs of entangled photons, the authors of the article prove that the state of these four photons can be expressed as shows the equation (2).
From now on, everything is a trick. If Victor has some apparatus that allows the measurement of his two photons in the Bell-base, then he gets one of the four states I mentioned above. The 4-photon wave-function COLLAPSES on one of these states, and because of the entanglement between the four photons, the state of the pair Alice's photon and Bob's photon, also collapses on the corresponding state.
However, WITH measurement or WITHOUT measurement, we can represent Victor's photons in the Bell base. The measurement done by Victor only gives us the information which one of the 4 possibility we would obtain on the respective pair that came to him. Thus, we can compare with the result of Alice and Bob. If Victor doesn't do this measurement we can't compare, s.t. the results of Alice and Bob seem to us uncorrelated.
But there is one more thing, and fundamental. It makes no difference who measured first, Alice and Bob, or Victor. These entangled particles DON'T CARE about space and time. For them, the question which particle was MEASURED FIRST has no meaning, it is always as if they are measured simultaneously. They have a way to arrange that their answers, a way that escapes our understanding. To us, it seems as if they communicate by superluminal messages. But we cannot lay hand on such messages.
Again, these particles behave according to another type of world that our space-time world. It is for us to investigate and try to understand it.
Did I help with my explanations?