I read parts of this book to complement the course taught on the same subject by the same author， since some proofs are left in the book and some exercises require information from the book but outside the lecture notes。 It was an excellent way of making you read materials from both lectures and reference texts。I suffered a lot in this course because it proved that my pure mathematics background （which exists） was so weak that I nearly failed every assignment （except one）。 This course really hel I read parts of this book to complement the course taught on the same subject by the same author， since some proofs are left in the book and some exercises require information from the book but outside the lecture notes。 It was an excellent way of making you read materials from both lectures and reference texts。I suffered a lot in this course because it proved that my pure mathematics background （which exists） was so weak that I nearly failed every assignment （except one）。 This course really helped me understand better what it takes to prove something， and that my intuition from differential geometry does not readily carry over here even though I did reasonably well in differential geometry classes。 However， I must admit that I think I learnt a lot from the book and the class， with many new concepts I have never seen e。g。 semi-definite programming was very difficult for me， but it was a very surprising way to solve some problems for me， and this was the first time I saw the Choi isomorphism and operator-vector correspondence that standard textbooks like Nielsen/Chuang did not cover。This book is a must-read for quantum information beyond Nielsen/Chuang level， and I am hoping to revisit this book again once my quantum information background has recovered/re-established。 If you managed to get through this book， you are probably ready for doing research-level problems for theoretical quantum information。 The author once said that a possible drawback of his book is his distinct choice of notation， but in all honesty I preferred his notation over standard ones （braket）。 Aside 1: unfortunately， as I was devastated by my near failure （I overestimated my ability to do pure math at that time）， I forgot and did not maintain this part of knowledge in me， including notations and everything。 What I would give to redo this course all over again and revisit this wonderful book。Aside 2: I am partially using this book here and there in 2020 to study for my qualifier to complement the parts in Nielsen/Chuang。 So I will unashamedly count the finishing date as 2020。 。。。more