2008/08/01 by Teiko Heinosaari, Mario Ziman · 1 citation
Computer Science · Physics and Astronomy · #Categorical quantum mechanics #Open quantum system #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum information #Quantum information science #Quantum operation #Quantum probability #Quantum process #Relativity and Gravitational Theory #quant-ph
paper · pdf · doi:10.2478/v10155-010-0091-y
published as Acta Physica Slovaca 58, 487--674 (2008) · 188 pages. Extension of lecture notes from a course that the authors gave in 2007/08 in Research Center for Quantum Information, Bratislava
openalex publication_date 2008/08/01 · arxiv created 2008/10/20 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Guide to mathematical concepts of quantum theory 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 self-containing explanation of the main concepts of the modern language of quantum theory.