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2016

Geometric and Information-Theoretic Properties of the Hoggar Lines

Stacey, Blake C.

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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.

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