Interestingly, a statistician colleague recently forwarded me the Silver et al. manuscript on quantum entropy, along with some related tech reports by the same authors. He was interested in possibly resurrecting their unpublished work; a top statistics journal was interested in an early version years ago, but the authors never revised it.

I only skimmed it and didn't follow the details, but I gather that the mathematical properties of quantum entropy act as some kind of "regularization" (e.g. imposing smoothness constraints) on maximum entropy inference. I told him that to write something up, he'd probably have to compare it against modern methods (e.g., in image processing spatial Bayesian models estimated with Gibbs sampling have emerged in subsequent years as competitors to MaxEnt). I'm not sure how in-vogue MaxEnt still is nowadays. I also mentioned I knew a blog where people discuss quantum entropy ...