Written and edited by leading researchers in the field, "The Physics of Quantum Information" still is a great introduction to quantum information.
The book starts with the basic concepts and experiments - superpositions, the Einstein-Podolsky-Rosen thought experiment, Bell's inequality, the Aspect experiments. Several chapters outline the basics, whys and wherefores of quantum cryptography, key experiments, future applications, open questions. The treatment of quatum computation is no less thorough.
Zeilinger's personal pet topic, quantum teleportation, and his key experiments are also laid out extensively. Like in the rest of the book, the presentation is clear, so even if you happen not to agree with all of the authors' conclusion, the chapter is well worth reading.
Since the book was published in 2000 and treats current science, some of the material is a bit outdated. Nevertheless, "The Physics of Quantum Information" serves as a superb introductionary course into the field - providing you start with a firm basis in quantum mechanics, i. e. have worked your way through Sakurai's "Modern Quantum Mechanics" or an equivalent course.
If neither physics nor computation is your trade, but you are interested in the field anyway, give John Gribbin's "In Search of Schrodinger's Cat" a try. If you have some scientific background, speak German, and just want an overview, Dagmar Bruß' "Quanteninformation" will suit your needs better.
But for serious studies at the postgraduate level, I recommend this book without hesitation.