Book for quantum information theory

Question

I am interested in a mathematical approach to quantum information theory. I have observed that several probabilists have been working in this area. What can be a suitable background and good book for this subject?

Answer 1

I myself started learning quantum information theory with Quantum Computing by J. Gruska and Quantum Computation and Information Theory by Nielsen-Chuang. I think the former is more mathematical. It covers very well Hilbert spaces and related notions. I like very much the treatment of observalbles and measurements. On the other hand Nielsen-Chuang, I think, has a very good computational approach.

In overall, if you look for an $\textbf{introduction}$, it will be difficult to find a lot of abstract math. I work in mathematical aspects of quantum error correction and the books I mentioned worked well for the basics. Afterwards most of literature was articles and lecture notes.

Answer 2

There's an excellent introductory book called "Quantum Computing for Computer Scientists" by Yanofski and Manucci. It goes through the theory of quantum computation and information using simple Hermetian matrices and tensor products as the mathematical language.