Quantum Information Theory (ETH Zurich)

ETH Zurich is consistently ranked among the world’s best technical universities, and its quantum information theory courses reflect the institution’s rigorous mathematical culture. The course materials cover quantum Shannon theory and information-theoretic aspects of quantum computing at a depth rarely found outside leading research universities.

ETH Zurich’s quantum information faculty includes researchers working at the frontier of quantum channel capacity theory, quantum thermodynamics, and quantum error correction. The course connects the formalism of quantum channels to deep results about what information can be reliably transmitted and processed in quantum systems.

What you’ll learn

• Quantum entropy: von Neumann entropy, conditional quantum entropy, quantum mutual information, and their operational interpretations in terms of data compression
• Quantum channels and their representations: Kraus operators, the Choi-Jamiolkowski isomorphism, and the relationship between different descriptions of quantum noise
• Classical capacity of quantum channels: the Holevo quantity, the HSW theorem, and the classical information capacity of noisy quantum channels
• Quantum capacity: coherent information, the LSD theorem, and the challenges of computing quantum capacity for general channels
• Quantum Shannon theory: single-letter versus regularised capacity formulas, superadditivity, and what it means for practical quantum communication
• Entanglement-assisted communication: how shared entanglement changes channel capacities and the elegant structure of the entanglement-assisted capacity theorem

Who is this for

Graduate students and researchers with a strong mathematical background who want to understand quantum information from an information-theoretic perspective. This material is particularly valuable for those interested in quantum communication, quantum networks, or the theoretical foundations of quantum computing. Students considering applying to ETH Zurich’s graduate programs will find this an accurate representation of the level of mathematical sophistication expected.

Prerequisites

Graduate-level linear algebra and functional analysis are required. A solid understanding of classical information theory, particularly Shannon entropy and channel capacity, is strongly recommended. Quantum mechanics at the undergraduate level and some familiarity with density operators will be assumed. This course is not suitable for beginners.