A generalization of majorization that characterizes Shannon entropy

Abstract

We introduce a binary relation on the finite discrete probability distributions which generalizes notions of majorization that have been studied in quantum information theory. Motivated by questions in thermodynamics, our relation describes the transitions induced by bistochastic maps in the presence of additional auxiliary systems which may become correlated in the process. We show that this relation is completely characterized by Shannon entropy H, which yields an interpretation of H in resource-theoretic terms, and admits a particularly simple proof of a known characterization of H in terms of natural information-theoretic properties.

10 pages; see also arXiv:1409.3258. v3: some typos corrected; close to published version

References in corpus (3)

• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation

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