TY  - BOOK
AU  - Skrzypczyk,Paul
AU  - Cavalcanti,Daniel
ED  - Institute of Physics (Great Britain),
TI  - Semidefinite programming in quantum information science
T2  - [IOP release $release]
SN  - 9780750333436
AV  - QC174.17.D37 S477 2023eb
PY  - 2023///]
CY  - Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK)
PB  - IOP Publishing
KW  - Quantum theory
KW  - Data processing
KW  - Semidefinite programming
KW  - Quantum physics (quantum mechanics & quantum field theory)
KW  - bicssc
KW  - SCIENCE / Physics / Quantum Theory
KW  - bisacsh
N1  - "Version: 202303"--Title page verso; Includes bibliographical references; part I. The fundamentals. 1. Linear programming -- 1.1. The basics -- 1.2. Geometric interpretation -- 1.3. Duality -- 1.4. Slack variables -- 1.5. Weak and strong duality -- 1.6. Concluding remarks -- 1.7. Advanced topics -- 1.8. Further reading; 2. Semidefinite programming -- 2.1. Primal semidefinite programs -- 2.2. Duality -- 2.3. Weak and strong duality -- 2.4. Complementary slackness -- 2.5. Linear programs as special instances of semidefinite programs -- 2.6. Concluding remarks -- 2.7. Further reading; part II. Semidefinite programming in quantum information science. 3. Quantum states -- 3.1. Quantum state estimation -- 3.2. The quantum marginal problem -- 3.3. Concluding remarks -- 3.4. Further reading -- 3.5. Advanced topics; 4. Quantum measurements -- 4.1. Quantum measurement estimation -- 4.2. Quantum state discrimination I -- 4.3. Quantum state discrimination II -- 4.4. Concluding remarks -- 4.5. Further reading -- 4.6. Advanced topics; 5. Quantum entanglement -- 5.1. Entanglement of pure and mixed states -- 5.2. The positive-partial-transpose criterion -- 5.3. Entanglement negativity -- 5.4. Random robustness of entanglement and SDP relaxations -- 5.5. k-symmetric extensions -- 5.6. Concluding remarks -- 5.7. Further reading -- 5.8. Advanced topics; 6. Measurement incompatibility -- 6.1. Joint measurability as an SDP -- 6.2. Two dichotomic measurements -- 6.3. Concluding remarks -- 6.4. Further reading -- 6.5. Advanced topics; 7. Quantum channels -- 7.1. The Choi-Jamio±kowski isomorphism -- 7.2. Channel estimation -- 7.3. The diamond norm and channel discrimination -- 7.4. The conditional min-entropy and the singlet fidelity -- 7.5. Concluding remarks -- 7.6. Further reading -- 7.7. Advanced topics; Graduate students and researchers in quantum information aiming at learning semi-definite programming; Also available in print
N2  - 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. Part of IOP Series in Quantum Technology
UR  - https://iopscience.iop.org/book/mono/978-0-7503-3343-6
ER  -