In ages past, biographers read the correspondence of their subjects to gain information. There was something pleasing about finding a new morsel about an old life, a letter turning up in an unexpected place. Now… Hey, I have a page on YouTube that I forgot about until today!
Insofar as the subject of any biography is a singular self, this is the same Blake Stacey as the
Someone or something else created the
page, on which I have twice as many editions as ratings. But I am not the Blake, Stacey who wrote the Boy’s Own Adventure story “The Derelict Hunters: A Thrilling Story of the Dread Sargasso Sea” (more’s the pity).
B. C. Stacey, “Geometric and Information-Theoretic Properties of the Hoggar Lines” (2016), arXiv:1609.03075 [quant-ph].
We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability distributions. Investigating the shape of this representation of state space yields a pattern of connections among a remarkable spread of mathematical constructions. In particular, studying the Shannon entropy of probabilistic representations of quantum states leads to an intriguing link between the questions of real and of complex equiangular lines. Furthermore, we will find relations between quantum information theory and mathematical topics like octonionic integers and the 28 bitangents to a quartic curve.
All things told, SIC-POVMs are just about the damnedest things I’ve ever studied in mathematics.
(Also listed on SciRate.)