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Measurement, Interpretation and Information
Open AccessArticle

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
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Author to whom correspondence should be addressed.
Academic Editor: Olimpia Lombardi
Entropy 2015, 17(11), 7349-7373; https://doi.org/10.3390/e17117349
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)
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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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.

AMA Style

Holik F, Bosyk GM, Bellomo G. Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory. Entropy. 2015; 17(11):7349-7373.

Chicago/Turabian Style

Holik, Federico; Bosyk, Gustavo M.; Bellomo, Guido. 2015. "Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory" Entropy 17, no. 11: 7349-7373.

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