Quantum information references

The best recommendation I can offer isn't for a book, but a series of video lectures. The Perimeter Institute and the University of Waterloo offer a Masters program in theoretical physics called Perimeter Scholars International (full disclosure: I graduated from PSI in 2010), and videos of all PSI lectures are posted on PI's video site, PIRSA. One of the PSI courses, Rob Spekkens' course on quantum foundations, sounds like it'd be the exact kind of thing you're looking for. The most recent offering of his class can be found here.

I'd recommend the lecture notes from these two courses taught by John Watrous. They can be found at http://www.cs.uwaterloo.ca/~watrous/lecture-notes.html from when he taught at the University of Calgary. I've used the notes from his Theory of Quantum Information course numerous times for a quick reference on some more difficult concepts.

Scott Aaronson has just published a new book about quantum computing. According to the nice introductary comments the author himself has written to his book here (scroll down to the second half of the article if you only want to learn about the book), it should explain and introduce both the physical and mathematical concepts quantum computing is based on.

Maybe reading this book can help students in choosing the appropriat mathematical and phyics lectures to be heard in what reasonable order to finally being able to do research in quantum computing too.

This answer contains some additional resources that may be useful. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary.

• Quantum Computer Science : An Introduction by Mermin is a really fine book. 'The clearest and most straightforward introduction that I've seen'.

• John Preskill's lecture notes, though it does not provide answers to its exercises.

• Lectures by H. Mabuchi at Stanford.

• Lectures by R. Sasaki.

• You might like quantiki http://www.quantiki.org/, it is a portal dedicated to quantum information theory. It contains interesting stuff ( e.g, video abstracts of papers).

• Nielsen, Chuang: Quantum Computation and Quantum Information.

• Bengtsson, Życzkowski, Geometry of Quantum States.

• Mark M. Wilde on quantum information (Shannon) theory on the arxiv: From Classical to Quantum Shannon Theory. It is essentially the same as his published book: Quantum Information Theory