acta physica slovaca 

Acta Physica Slovaca 58, No.4, 487674 (2008) (187 pages)
Guide to mathematical concepts of quantum theory Teiko Heinosaari and Mário Ziman Department of Physics, University of Turku, FI20014, Finland Research Center for Quantum Information, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia Full text: ::pdf :: (received 9.10.2008, accepted 14.10.2008) Abstract: Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and selfcontaining explanation of the main concepts of the modern language of quantum theory. PACS: 03,65.w, 03.67.a,03.65.Ta Keywords: Quantum theory, Quantum measurement, States, Effects, Observables, Channels, Instruments, Entanglement 
ISSN 1336040X (online) ISSN 03230465 (printed) For authors: ActaStyle.cls 
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