It has been almost 12 years since we wrote the preface to the first edition of this book. Again we are sitting in the barrel vault basement of Physikzentrum at Bad Honnef near Bonn, Germany. We both do not feel so much differently – but the field of quantum information, many topics of which are covered in this book, has progressed enormously. We are currently witnessing the dawn of the European Quantum Technology Flagship. The field has come a long way, with sizeable activities in many countries worldwide.

Occasionally the memory of Thomas Beth comes back, and we are sure that he would have loved to see the flourishing of the field he was so fond of and which he pushed so much as a computer scientist. All in all, it seems timely to reedit the book.

Some chapters (3, 6, 11–13, 16, 20, 22–23, 29–31, 33, and 37) are left unchanged, which is no surprise as the basic foundations are what they are.

Other chapters (1–2, 4–5, 7–8, 10, 14–15, 17–19, 21, 24–25, 28, and 34–35) were rewritten to account for the recent developments; there are also some new chapters (9, 26–27, 32, 36, and 38).