Springer, 2019. — 177 p. — (Lecture Notes of the Unione Matematica Italiana 25). — ISBN 978-3-030-06121-0.The development of quantum mechanics has been one of the greatest scientific achievements of the early twentieth century. In spite of its remarkable success in explaining and predicting an amazing number of properties of our physical world, its interpretation has raised strong controversies among a wide community of scientists and philosophers. One of the hottest points of discussion is the meaning of the socalled quantum entanglement that, for systems of two or many particles, allows in particular the possibility for each particle of the system to be simultaneously located at different spatial positions. Contents Introduction A Very Brief Introduction to Quantum Computing and Quantum Information Theory for Mathematicians Entanglement, CP-Maps and Quantum Communications Frontiers of Open Quantum System Dynamics Geometric Constructions over C and F2 for Quantum Information Hilbert Functions and Tensor Analysis Differential Geometry of Quantum States, Observables and Evolution
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