A generalization of majorization that characterizes shannon entropy
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 presen...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
11 February 2016
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| In: |
IEEE transactions on information theory
Year: 2016, Volume: 62, Issue: 4, Pages: 1711-1720 |
| DOI: | 10.1109/TIT.2016.2528285 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1109/TIT.2016.2528285
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| Author Notes: | Markus P. Müller and Michele Pastena |
| Summary: | 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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| Item Description: | Gesehen am 02.10.2020 |
| Physical Description: | Online Resource |
| DOI: | 10.1109/TIT.2016.2528285 |