Entropic bounds on the quantum marginal problem

Do you have any unpublished results?

Do you want to share them but don’t have the motivation, time, and/or energy to carry them through to publication?

Do you want an easy simple way to bring your work to a wider audience?

Yes, yes, and yes!

I am always on the lookout for cheap, easy, and painless ways to avoid hard work. Thus it was that I had the idea of making videos explanations of old unpublished results: I figured that since it is really easy to explain something on a board, it must follow that with a cheap video camera and a spare 20 minutes it must be easy to make videos.

Well, ok, it turns out that it isn’t so simple because it is actually rather hard work to make a not-complete-piece-of-crap video.

Today I’d like to announce a youtube video experiment aimed at finding a good way to communicate unpublished results that are still interesting. The purpose of this video is to explain the basic idea behind a paper I wrote in 2008 that I feel, sadly, will never be published (due in part to unbelievably hostile referee reports and a subsequent lack of motivation on my part). The paper in question contains a simple bound on the number of independent solutions to the quantum marginal problem, which is of central importance in quantum information theory.

If you are interested in learning more about the quantum marginal problem I can happily recommend checking out this talk and this blog post. Also take a look at this thesis and overview, the gaussian version, a powerful solution, and an intuitive solution of the simple subcase. Also check out this cool application. There have been some further progress on using entropic bounds in this recent paper.

Sadly the video production equipment I had on hand simply wasn’t as good as it should be: I’ve now learnt the hard way that one should invest in a good microphone and a camera that isn’t 8 years old… (Probably a smartphone would’ve done a better job…) I’ve since corrected this and in my next videos I hope to improve the sound and picture quality to at least an acceptable level…

Please like the video if it is something you want to see more of, dislike it if you think it was terrible, and please do subscribe if you want to see more!

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