A Generalization of Majorization that Characterizes Shannon Entropy
2016
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.
Keywords:
- Entropy in thermodynamics and information theory
- Discrete mathematics
- Information diagram
- Joint quantum entropy
- Combinatorics
- Rényi entropy
- Limiting density of discrete points
- Min entropy
- Maximum entropy thermodynamics
- Shannon's source coding theorem
- Mathematics
- Quantum relative entropy
- Entropy power inequality
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