期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 56, 期 9, 页码 4674-4681出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2010.2054130
关键词
Conditional entropies; quantum information; smooth entropies
资金
- Swiss National Science Foundation [200021-119868]
- Swiss National Science Foundation (SNF) [200021-119868] Funding Source: Swiss National Science Foundation (SNF)
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two entropy measures, called smooth min-entropy and smooth max-entropy, respectively. While both entropies are equal to the von Neumann entropy in certain special cases (e. g., asymptotically, for many independent repetitions of the given data), their values can differ arbitrarily in the general case. In this paper, a recently discovered duality relation between (nonsmooth) min- and max-entropies is extended to the smooth case. More precisely, it is shown that the smooth min- entropy of a system conditioned on a system B equals the negative of the smooth max-entropy of conditioned on a purifying system C. This result immediately implies that certain operational quantities (such as the amount of compression and the amount of randomness that can be extracted from given data) are related. We explain how such relations have applications in cryptographic security proofs.
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