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Kvantové štruktúry a teória kategórií

Roman Frič

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The methods and constructions of category theory are suitable tools for studying quantum structures and
generalized probability. The aim of the present paper is to support our claim via several examples and to motivate further
research in this area.

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The methods and constructions of category theory are suitable tools for studying quantum structures and generalized probability. The aim of the present paper is to support our claim via several examples and to motivate further research in this area.

•Jan 1, 2004•0 citations

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Quantum Probabilities

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Theory of Generalized Measures and Applications Generalized Measures on Quantum Structures and Entropy

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•Jan 1, 2015•1 citation
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The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out non-classical features of single systems can equivalently result from higher dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features.