Some operator monotone functions

Frank Hansen

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arXiv · 0803.2364

Some operator monotone functions

Frank Hansen

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Abstract

We prove that the functions t -> (t^q-1)(t^p-1)^{-1} are operator monotone in the positive half-axis for 0 < p < q < 1, and we calculate the two associated canonical representation formulae. The result is used to find new monotone metrics (quantum Fisher information) on the state space of quantum systems.

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Frank Hansen. 2008-10-14. Some operator monotone functions. https://arxiv.org/abs/0803.2364

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