Entropy Distance: New Quantum Phenomena

Details Entropy Distance: New Quantum Phenomena Entropy Distance: New Quantum Phenomena

2010-07-30

arxiv.org/abs/1007.5464v2

Physics

Mathematical Physics

16 pages, 5 figures

Scientific paper

The relative entropy distance of a state from an exponential family is important in information theory and statistics. The class of exponential families is parametrized by a Grassmannian. A minimal example in the algebra of complex 3x3 matrices shows that the mean value set of an exponential family has typically non-exposed faces. Where non-exposed faces are born in the Grassmannian, families have a discontinuous entropy distance. These two phenomena are related to three distinct closures, which all coincide in the probabilistic case of the algebra $\mathbb{C}^N$. A necessary condition for a local maximizer of the entropy distance is calculated in a finite-dimensional complex matrix algebra.

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