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Entropy 2015, 17(11), 7349-7373; doi:10.3390/e17117349

Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory

1
Instituto de Física La Plata (IFLP), CONICET, 115 y 49, 1900 La Plata, Argentina
2
Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina
*
Author to whom correspondence should be addressed.
Academic Editor: Olimpia Lombardi
Received: 31 August 2015 / Revised: 19 October 2015 / Accepted: 20 October 2015 / Published: 28 October 2015
(This article belongs to the Special Issue Information: Meanings and Interpretations)
View Full-Text   |   Download PDF [820 KB, uploaded 28 October 2015]   |  

Abstract

In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures. View Full-Text
Keywords: quantum probability; generalized majorization; information theory; quantum information quantum probability; generalized majorization; information theory; quantum information
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Holik, F.; Bosyk, G.M.; Bellomo, G. Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory. Entropy 2015, 17, 7349-7373.

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