Semidefinite programming in quantum information science /

---

"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 reading2. 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 readingpart 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 topics4. 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 topics5. 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 topics6. 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 topics7. 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.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.Graduate students and researchers in quantum information aiming at learning semi-definite programming.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.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.Title from PDF title page (viewed on March 31, 2023).

---

Availability

No copy data

Detail Information

Series Title

-

Call Number

-

Publisher

: .,

Collation

1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750333436

Classification

530.1/2/02855369

Content Type

-

Media Type

-

Carrier Type

-

Edition

-

Subject(s)

SCIENCE / Physics / Quantum Theory.
Quantum theory
Semidefinite programming.

Specific Detail Info

-

Statement of Responsibility

Paul Skrzypczyk, Daniel Cavalcanti.

Other version/related

File Attachment

Comments

---

You must be logged in to post a comment