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BENTHAM SCIENCE PUBLISHERS eBooks

Entanglement and Entropy

Published Dec 11, 2013• 0 citations
Publisher

Abstract

We review links between the entanglement concept and the entropic-information one, as represented by different measures like the Shannon and Tsallis ones. This remarkable linkage illuminates several aspects of the physics of information-theoretic activity and it is thus of importance to understand the structure of the concomitant connections

DOI
10.2174/9781608057603113010015

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We review links between the entanglement concept and the entropic-information one, as represented by different measures like the Shannon and Tsallis ones. This remarkable linkage illuminates several aspects of the physics of information-theoretic activity and it is thus of importance to understand the structure of the concomitant connections
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Abstract Entropic uncertainty relations are studied from the conceptual viewpoint and in the context of various applications. Providing as tight inequalities as possible is thus an important issue. Measurements of special types are indispensable in quantum information science. Their structure allows us to estimate the index of coincidence. Uncertainty relations follow an estimation of entropies at the given index of coincidence. Relations of such a kind are a known issue in information theory. It concerns links between different information measures. Information diagrams are a tool to study relations between two utilized characteristics. A search for improved inequalities uses the index of coincidence as the abscissa and the entropy of interest as the ordinate. This approach before dealt with standard information functions assigned to the Shannon entropy. But generalized entropies often reveal new links between information measures. This paper applies the method of information diagrams to the Rényi and Tsallis entropies. Such entropies and related information functions have found use in quantum information theory. Improved estimates of the Tsallis and Rényi entropies at the given index of coincidence are obtained. Hence, new entropic uncertainty relations for specific types of measurements follow. They include mutually unbiased bases, symmetric informationally complete measurements, and equiangular tight frames.