Overview

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum information science. Following a review of the theory of semidefinite programming, the book proceeds to describe how it can be used to address a wide range of important problems from across quantum information science. Specific applications include quantum state, measurement, and channel estimation and discrimination, entanglement detection and quantification, quantum distance measures, and measurement incompatibility. Though SDPs have become an increasingly important tool in quantum information science it’s not yet the kind of mathematics students learn routinely. Assuming only a basic knowledge of linear algebra and quantum physics and quantum information, this graduate-level book provides a unified and accessible presentation of one of the key numerical methods used in quantum information science. Whilst the focus is on the theoretical machinery of SDPs, the authors have provided an accompanying GitHub repository containing example code, covering some of the SDPs studied in this book. Key features Accessible for graduate students in science and mathematics A unified and accessible presentation of one of the key numerical methods used in quantum information science Written by leading researchers on the topic Accompanying GitHub repository with sample code

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"""SDP is becoming an increasingly important tool in quantum information science. The techniques are ‘standard for experts’ but they are not taught routinely … a dedicated treatise introducing this will be a great resource for the years to come … The authors are among the very best in this field.""- Nicolas Brunner, Université de Genève."

Author Information

Paul Skrzypczyk is currently an Associate Professor and Royal Society University Research Fellow at the University of Bristol in the School of Physics. He obtained his PhD in Theoretical Physics from the University of Bristol in 2011, under the supervision of Professor Sandu Popescu, with his PhD studies focusing on quantum nonlocality and quantum thermodynamics. He carried out postdoctoral research at the University of Cambridge, and ICFO--The Institute for Photonic Sciences, before returning to Bristol in 2015. In 2016 he was awarded a Royal Society University Research Fellowship and became a lecturer in 2018 and an Associate Professor in 2022. Paul's research interest span many areas of quantum information and quantum foundations, ranging from quantum nonlocal effects, such as Bell nonlocality, quantum steering and quantum teleportation, to quantum measurements and measurement incompatibility, to quantum thermodynamics. Convex geometry, semidefinite programming and convex optimisation have been the primary mathematical tools used in his research over the years. Daniel Cavalcanti is currently a senior researcher at Algorithmiq Ltd. He obtained a PhD in Theoretical Physics at ICFO--Institute of Photonic Sciences in 2008 on the topics of entanglement and characterisation of quantum correlations. After a short postdoc at ICFO in 2009, he joined the Centre for Quantum Technology (Singapore) in 2010, first as a postdoc in Professor Valerio Scarani's group, and soon as an independent researcher. In 2013 he returned to ICFO, where he stayed until 2021 on a Ram\'on y Cajal grant. Daniel's research has focused on quantum foundations, quantum correlations, quantum communication and, more recently, quantum computation. Daniel also holds a master's degree in graphic design and runs Bitflow, a graphic design studio dedicated to science and technology-related projects.

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