期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 61, 期 3, 页码 1458-1473出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2387822
关键词
Relative entropy; entropy inequalities; channel capacity; surprisal; thermodynamics; heat capacity
资金
- Marie Curie Intra-European Fellowship QUINTYL within the European Union Framework Programme 7 [298742]
- Alfried Krupp von Bohlen und Halbach-Stiftung
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any prescribed value of the entropy difference, both for quantum and classical systems. We outline implications for information theory and thermodynamics, such as a necessary condition for a process to be close to thermodynamic reversibility, or an easily computable lower bound on the classical channel capacity. Furthermore, we derive a tight upper bound, uniform for all states of a given dimension, on the variance of the surprisal, whose thermodynamic meaning is that of heat capacity.
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