Again, in the interests of keeping all things C-field in one place, I include the following excerpts from comments on another thread.
Florin Moldoveanu replied on Mar. 25, 2011 @ 04:39 GMT
Dear Edwin,
I located the paper on the archive and I read it. I believe it got accepted to PRL not because of Entangelment Sudden Death-ESD (which was already known) but due to the fact of being calculated for optical fibers for the first time.
A nice geometrical explanation for ESD can be found here: http://iopscience.iop.org/1367-2630/9/7/237/fulltext and a larger exposition on entangelment in general is found in this book: http://www.amazon.com/Geometry-Quantum-States-Introduction-Entanglement/dp/0521814510
I don't think there is any foundational mistery here. There are mathematical methods to test the presence of entangelment, and under some circumstances, entangelment vanishes even though cohererence does not. The sudden death is only apparent though as there are unitary operations (local operations which can be applied on the systems) which can revive it just as sudenly. Al long as cohererence is not lost, entangelment "death" is only apparent.
Edwin Eugene Klingman replied on Mar. 25, 2011 @ 22:11 GMT
Dear Florin,
Thanks for looking at the 'ESD' paper and thanks for the ESD references. Can you explain very simply what you mean by "already know that contextual HV theories are bypassing all no-go theorems".
You say, "I don't think there is any foundational mistery here. There are mathematical methods to test the presence of entangelment, and under some circumstances, entangelment vanishes even though cohererence does not. The sudden death is only apparent though as there are unitary operations (local operations which can be applied on the systems) which can revive it just as sudenly. Al long as cohererence is not lost, entangelment "death" is only apparent."
The PRL paper states that "decoherence that takes place when the entangled quantum systems interact with the environment" and "optical birefringence is a major polarization decoherence mechanism." Further "In the simplest case in which PMD is present only in one of the fibers...[there is] unconditional violation of Bell's inequality."
This is **exactly** what I claimed in my essay, but was challenged by several and supported by none!
It complicates the issue to consider special cases and the fact that 'additional unitary operations' may succeed in re-entangling the system. You may not consider it 'fundamental' but when the 'knowledgeable physicists' challenge my claim that "photons can change en route" and I produce recent Phys Rev Letter proof that they do, and that this "unconditionally" violates Bell's inequality [my claim!] and Zeilinger's logic, I consider it significant.
Edwin Eugene Klingman
Florin Moldoveanu replied on Mar. 26, 2011 @ 01:52 GMT
Dear Edwin,
Please see this: http://www.mth.kcl.ac.uk/~streater/lostcauses.html#I
Citing from there, a contextual theory means the following:
Suppose Alice and Bob measure either 2 compatible observables: X and Y or 2 compatible observables X and Z. Moreover, Y and Z are complemetary: one can measure either one, but not both. The question is how to treat observable X: contextual or non-contextual. Non-contextual means that the X in both settings (XY and XZ) is described by the same thory. Contextual means that the X in XY and XZ is described by two different theories. Non-contextual hidden variable theories obey Bell's inequality and they are rulled out by experiments. Contextual hidden variable theories do not obey Bell's inequality and they are not rulled out by experiments. However, contextual models do not have an "objective reality" property as they change depending on the measurement contex. Yes, the Moon may be there even when we do not see it, but in contextual theories, the Moon is made of cheese if I look at it through sunglases, and is made of rocks when I observe it through a telescope. It is not the same object. It is "contextual".
About "changing on route", this is not what ESD is about. Indeed, the photon does not change, it only interacts with its environment. And entanglement is still there only hidden because it can be restored (by a unitary operation). A unitary operation is not unlike a rotation of a physical object. Take a piece of paper. From straight up it is a rectangle. Rotate it 90 degrees on the direction of viewing and (if the paper is straight) you see only a line segment. You may call it a "Sudden Death of the Area", but the area is still there. Rotate it some more and it will "come back". Conceptually this is the same with ESD, only that there you work in a complex space, and you have a unitary transformation, instead of an orthogonal one. This is precisely what paper about the geometry of ESD was trying to explain.
