This lecture will introduce important concepts of quantum information theory with a focus on entanglement theory.
Preliminary list of topics:
- Recap of QM formalism: states and operators, density operator, composite systems, Schmidt decomposition, quantum measurement
- Quantum operations: environments, Kauss channels, CPTP maps, Choi–Jamiolkowski isomorphism
- Distance measures: classical and quantum distance measures, trace distance, Bures distance, etc.
- Entropy and information: Shannon and von Neumann entropy, conditional quantum entropy and coherent information, quantum mutual information, quantum source coding, accessible information and the Holevo bound
- Entanglement theory: mixed-state entanglement, LOCC and SEP, majorization and Nielsen’s theorem, entanglement distillation and entanglement cost, entanglement measure, entanglement witnesses
