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

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.

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Cited by in corpus (9)

• Quantum Probabilities as Behavioral Probabilities
• Exact Shannon entropies for the multidimensional harmonic states
• Non-deterministic semantics for quantum states
• Lattices and Their Consistent Quantification
• Generalized entropies in quantum and classical statistical theories
• Logical structures underlying quantum computing
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Majorization and dynamics of continuous distributions
• Pattern Recognition In Non-Kolmogorovian Structures