Dear Akbar,
I'm a fellow contestant in the FQXi essay contest. I just read your essay
and posted some remarks on your thread. Since there had not been much
activity there recently, I decided to email you as well (it's a better
method of communication anyway).
I enjoyed your essay, and I believe I will find your analysis quite useful
for some of my own work. You frame the problem magnificently with
excellent referencing and historical context. Although I am not quite
clear on the exact scope of what you have proven (see below), your work
rates highly in my opinion. A few more thoughts.
1. Thank you for the reference [31] concerning graph states. This is
helpful for some of my own (unpublished) quantum-information theory work.
2. I also appreciate the discussion of non-local boxes and related issues
(pages 2-3).
3. I am trying to understand exactly how general your conclusions are in
section IV. You calculate a particular example involving the TB protocol,
but the discussion in the first two paragraphs of the section make it seem
as though you have considered many different models and come to similar
conclusions.
4. You conclude by noting that the arguments you present indicate the
necessity for a deeper understanding of the notions of non-locality,
reality, and entanglement. An idea that might partially contribute to
this is as follows. The two possible explanations for violation of
Bell's inequalities that you mention in the second paragraph of section IV
involve metric and order-theoretic properties of spacetime. Nonlocality
in this context is obviously a metric property, because distance is
measured by the metric. Preexistence (of quantum measurement results)
involves time and order. The reason I raise these points is because I
believe satisfactory understanding of these issues may ultimately depend
on knowledge of spacetime microstructure. For instance, if manifold
structure breaks down on small scales, a different definition of locality
(independent of a metric) will be necessary. One possible way to define
locality would be to take two systems to be mutually local if they
actually do interact. From this viewpoint, "quantum nonlocality" might
be merely a natural manifestation of non-manifold structure.
I present my own favorite idea for such structure in my essay (topic
1386). If you have time to read it, I'd appreciate your thoughts.
Thanks for the great read! Take care,
Ben Dribus