This course is meant for Master’s and starting Ph.D. students with an interest in theoretical quantum information.
It opens with the necessary linear algebra groundwork — Hilbert spaces, linear operators, tensor products, and Hermitian operator decompositions — before developing the full quantum formalism. From there, it explores quantum correlations through the lens of two-party games, including the CHSH game, Tsirelson’s bound, and Mermin magic squares. The next chapter covers entropy and information-theoretic quantities and culminates with the quantum Leftover Hashing Lemma. It then turns to Quantum Key Distribution (QKD), analysing security, privacy amplification, error correction, parameter estimation, and asymptotic key rates. The latter half of the course addresses more advanced topics in quantum communication: source coding and the convex-split lemma, quantum state splitting (with achievability and converse bounds), quantum state merging, channel coding with position-based decoding (for quantum, classical-quantum, and classical-classical channels), and finally quantum state redistribution.
The complete lecture notes are available in a single file (pdf).