[HTML][HTML] Quantum information as a non-Kolmogorovian generalization of Shannon's theory

F Holik, GM Bosyk, G Bellomo - Entropy, 2015 - mdpi.com
Entropy, 2015mdpi.com
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 …
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.
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