Methods for Quantum Technologies: Theory and Applications

Oral exam

Good knowledge of quantum mechanics and linear algebra. Familiarity with basic concept of quantum information, such as trace distance, fidelity, quantum channels, etc.

Part I: Classical and quantum hypothesis testing. Quantum relative entropies. Quantum Stein's lemma via the Golden-Thompson inequality and asymptotic spectral pinching (weak converse only).

Part II: Classical communication over quantum channels. Pretty good measurement and Barnum-Knill theorem. One-shot proof of the Holevo-Schumacher-Westmoreland theorem on classical capacity.

Part III: One-shot quantum relative entropies. Strong converse to the quantum Stein's lemma.

Part IV: Introduction to entanglement distillation. Breeding protocol and coherent information. Decoupling technique. One-shot hashing bound and asymptotic hashing bound on the one-way distillable entanglement. From entanglement distillation to quantum communication: proof of the Lloyd-Shor-Devetak theorem on quantum capacity.

Depending on the time, some additional topics may be covered: semi-definite programs for quantum information theory, Rényi relative entropies, etc.

Khatri and Wilde, Principles of Quantum Communication Theory: A Modern Approach. Available at https://arxiv.org/abs/2011.04672.