Geometry of Quantum States

The second edition of a book that has become a standard reference for researchers working on geometric aspects of quantum entanglement and quantum theory of information. Its comprehensive style makes it suitable for students of physics, information science, and mathematics wishing to learn more about quantum mechanics and quantum entanglement.

Preface; 1. Convexity, colours, and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Discrete structures in Hilbert space; 13. Density matrices and entropies; 14. Distinguishability measures; 15. Monotone metrics and measures; 16. Quantum entanglement; 17. Multipartite entanglement; Appendix 1. Basic notions of differential geometry; Appendix 2. Basic notions of group theory; Appendix 3. Geometry - do it yourself; Appendix 4. Hints and answers to the exercises; Bibliography; Index.