402-0462-00L Advanced Topics in Quantum Information Theory
| Semester | Frühjahrssemester 2022 |
| Dozierende | L. Pacheco Cañamero B. del Rio, R. Silva |
| Periodizität | jährlich wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
| Kurzbeschreibung | Solid introduction on advanced topics in quantum information theory, including: quantum thermodynamics, quantum clocks and control, measurement theory, quantum learning theory and quantum foundations. Pre-requisites: Quantum Information Theory or equivalent courses. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | To prepare master students for a PhD or industry career by providing a selection of active research topics in quantum information theory and related areas. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | 1. Quantum thermodynamics a) Virtual qubits, virtual temperatures b) Qubit swaps c) Passivity and complete passivity d) Equilibration, Jaynes principle, thermal states and baths e) Resource theories: noisy operations, majorization and entropy f) Resource theories: thermal operations, thermal majorization and free energy g) Maxwell’s demon and Szilard’s engine, Landauer erasure h) Thermodynamics protocols for finite-size systems i) Autonomous thermal machines: master equation, continuous dynamics, steady states j) Autonomous thermal machines: types of engines, working regimes 2. Clocks and control a) Ideal quantum clocks b) Quasi-ideal clocks c) Information-theoretical analysis 3. Puzzles and no-go theorems a) Hardy’s experiment (setup, simplified version, logical analysis) b) Quantum pigeonhole experiment (setup, simplified version, logical analysis) c) Physical implementation of measurements (von Neumann measurement scheme, strong and weak measurements, weak values) d) Replacing counterfactuals with weak measurements (Hardy and pigeonhole experiments) e) Replacing counterfactuals with measurements by different agents (Frauchiger-Renner experiment) f) Pre- and post-selection paradoxes: definition and example g) Contextuality: operational definition and relation to paradoxes 4. Quantum learning theory (guest lecturer Marco Tomamichel) Quantum learning theory provides the theoretical foundations for machine learning involving quantum objects, where the quantum aspect can either come from the learner itself (e.g. quantum algorithms for machine learning) or the object to be studied (e.g. state tomography), or both. Quantum information theory tools can establish fundamental limits for such learning tasks. We will in particular explore applications of information theory to the following learning tasks: a) Sample-optimal learning of quantum states b) Quantum PAC learning c) Multi-armed quantum bandits | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Provided for the majority of contents; hand-written lecturer notes for the rest. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | Selected papers will be recommended to read throughout the semester. For example, for the quantum learning part: [1] Haah et al., Sample-optimal tomography of quantum states, arXiv:1508.01797. [2] Arunachalam and de Wolf, Optimal Quantum Sample Complexity of Learning Algorithms, arXiv:1607.00932. [3] Lumbreras et al., Multi-armed quantum bandits: Exploration versus exploitation when learning properties of quantum states, arXiv:2108.13050. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Quantum Information Theory or equivalent course is necessary. Students should be familiar with density matrices, quantum channels (TPCPMs), Hamiltonian evolution and partial trace. Familiarity with quantum entropy measures helps but is not strictly necessary. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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