The rigorous framework beyond pure states and unitaries: density matrices, quantum channels, POVMs, entropy, distance measures and channel capacities.
Why it matters
Real systems are noisy and open, which means mixed states and channels. Every serious paper on error correction, cryptography or hardware characterisation assumes this machinery.
After this you will be able to
Hand-picked and ordered. If you only have time for one, take the first.
The mathematically complete treatment of channels, entropies, distance measures and semidefinite programming duality. Free PDF, and the reference when you need a theorem stated exactly right.
Preskill's notes have taught much of the field. Chapter 10 on quantum error correction is, for many researchers, the definitive introduction to the subject.
The standard graduate text on quantum information theory, building from classical Shannon theory to quantum channel capacities. Free on arXiv, and unusually readable for the depth it reaches.
Optional but clarifying. Quantum computing does not require a physics course, but if you want to know where the postulates come from rather than accepting them, start here.
Universally called "Mike & Ike" and still the field's reference text after two decades. Comprehensive rather than gentle — use it as the book you look things up in, not the one you read cover to cover first.
Researchers at Caltech’s quantum institute writing about their own work and field culture. Useful for understanding what doing quantum research is actually like day to day.
The standard Python library for simulating open quantum systems: density matrices, Lindblad master equations, noise models. Where you go when pure-state circuit simulators stop being enough.