Stochastic domination for iterated convolutions and catalytic majorization

Abstract

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 ${\mu }^{\ast n}$ is stochastically dominated by ${\nu }^{\ast n}$ for two given probability measures $\mu$ and $\nu$. As a consequence we obtain a similar theorem on the majorization order for vectors in ${\mathbb{R}}^d$. In particular we prove results about catalysis in quantum information theory.

References in corpus (3)

• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• Catalytic majorization and ${\ell }_p$ norms

Cited by in corpus (7)

• Catalytic quantum teleportation and beyond
• Catalysis of entanglement and other quantum resources
• Catalytic majorization and ${\ell }_p$ norms
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• The multiplicative property characterizes ${\ell }_p$ and $L_p$ norms
• Characterizing the asymptotic and catalytic stochastic orders on topological abelian groups
• Symmetric polynomials and $l^p$ inequalities for certain intervals of $p$