Methods for Quantum Technologies: Theory and Applications
Prerequisiti
Good knowledge of quantum mechanics and linear algebra. Familiarity with basic concept of quantum information, such as trace distance, fidelity, quantum channels, etc.
Programma
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.
Obiettivi formativi
Understanding the ultimate limits of quantum hypothesis testing tasks and how they are characterised by relative entropies. Appreciate the connection between quantum hypothesis testing and communication tasks over quantum channels, and how the ultimate limits on the latter can be calculated by means of the understanding of the former.
Riferimenti bibliografici
Khatri and Wilde, Principles of Quantum Communication Theory: A Modern Approach. Available at https://arxiv.org/abs/2011.04672.