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This book provides an accessible text for graduate students and those new to quantum information aiming to learn the basics of SDPs in quantum information science. Readers will be able to identify when a problem can be cast or approximated by an SDP and to master the main techniques to solve such problems. Moreover, the book will also give an overview of important problems in quantum information science, using a language that is accessible for those having basic knowledge on linear algebra and quantum mechanics.
Starting with linear optimization, a special case though one which his relatively well-known and mathematically simpler, the book proceeds to a technical definition of semi-definite programming, and in particular introduce the powerful tool of duality, and an introduction to the so-called dual problem . For this part the reader is only required to have basic knowledge of linear algebra, making it accessible for the majority of students and researchers in physics, engineering, and mathematics.
The book then proceeds to describe how different problems in quantum information can be solved exactly, or approximately by SDPs. In particular: the characterisation of quantum correlations, such as entanglement, quantum steering and non-locality, the characterisation of quantum measurements (measurement incompatibility and informativeness), quantum state discrimination, state estimation, the marginal problem, and quantum teleportation. Accompanied by Matlab ™ codes and Jupyter notebooks that can be directly used in these problems and allow readers to put the techniques covered into practice.
