Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 62, Issue 4, Pages 1711-1720Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2016.2528285
Keywords
Majorization; quantum information; Shannon entropy; thermodynamics
Funding
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
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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.
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