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

HOLIK, FEDERICO; BOSYK, GUSTAVO MARTÍN; BELLOMO, GUIDO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Lugar: Basel; Año: 2015 vol. 17 p. 7349 - 7373

1099-4300

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.