Before Professor Lidar and I dive into optimization, I’m trying to reproduce the results found in Table 1 of the Invisible Quantum Tripwire paper, specifying the efficiency of the IFM procedure for various settings of the parameters (number of times the photon cycles through the interferometer, total phase rotation angle, and amount of loss in the detection arm).
I’ve been iterating back and forth between Mathematica and my own simplifications, trying to clean up the formulas that feed into the efficiency calculation so that we can analyze them further.
Unfortunately, I’m currently frustrated by two problems that I’ve poured about six hours into now.
First, I’ve successfully reproduced the probabilities of all the various experimental outcomes, but when I collect them together and calculate the Chernoff distance C2 found on page 3, my values are consistently higher than the authors’. I’ve checked and re-checked my work and I can’t find any mistakes. Either there is a misprint in the article or I’m incorrectly using some function in Mathematica. I emailed the authors, asking for their code, and I’ll also try to consult with a Mathematica veteran. (Another pair of eyes would be really helpful right now.)
Second, I’m trying to perform an eigendecomposition of the evolution matrix. The eigenvalues I obtained by simplifying Mathematica’s symbolic calculation and plugging in the parameters I’m using match up with those yielded directly by a numerical Mathematica calculation. However, the eigenvectors don’t. For some reason, Mathematica returns a different set of eigenvectors, depending on whether I calculate symbolically and then substitute parameters, or whether I substitute parameters and then calculate numerically.
At this point, I’m out of ideas until I find a fresh pair of eyes to confirm that I’m not doing something crazy.
Send me your notebook? I’m quite a Mathematica hand these days. Errors in published papers are not all the uncommon, much more frequent than I, as a starry-eyed undergraduate, would have expected. While peer review is a brilliant idea, in practice it seems there isn’t always enough time to review things as closely as one should.
My undergrad naivety has too been shattered. It turned out that the authors had a significant typo in their equations and they’ve since corrected it.
Just as when I was three I assumed my dad was near God-like in his knowledge of the world, I always thought scientific papers were… right. Or at least if they were wrong, they expressed some kind of uncertainty (“We think this is what’s going on”). Nay! Its looking like theres plenty of stuff in papers thats just plain wrong.
This speaks to the importance of two things: (1) open peer review and (2) providing code/calculations to back up any claims made in a paper.
Oh and thanks for the offer though! With the current projects I’m working on, I’m quickly becoming a Mathematica power user, so I’m sure you’re expertise will be helpful in the future.