Stochastic domination for iterated convolutions and catalytic majorization

Details Stochastic domination for iterated convolutions and catalytic majorization Stochastic domination for iterated convolutions and catalytic majorization

2007-07-02

arxiv.org/abs/0707.0211v2

Physics

Quantum Physics

Scientific paper

We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer $n$ such that $\mu^{*n}$ is stochastically dominated by $\nu^{*n}$ for two given probability measures $\mu$ and $\nu$. As a consequence we obtain a similar theorem on the majorization order for vectors in $\R^d$. In particular we prove results about catalysis in quantum information theory.

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