# PHYSICS 491: Symmetry and Quantum Information

Department of Physics, Stanford University

*Schedule:* Tue & Thu 3:00 PM - 4:20 PM, Sapp 118 (Spring 2017)

*Instructor:* Michael Walter

*Office hours:* Wed 9:00 AM - 10:30 AM, Varian 358

This course gives an introduction to quantum information theory, targeted to advanced undergraduates and graduate students that have taken a graduate mechanics class on the level of Physics 230. We use symmetries as a guiding principle as well as as a toolbox to study the fundamental features of quantum mechanics and their exploitation for information processing tasks. See here for the syllabus.

Piazza is the primary source for all course material. You are encouraged to post your questions there.

## Lecture notes

- Lecture 1: Quantum correlations, non-local games, rigidity [pdf] [pdf]
- Lecture 2: Measurements, symmetric subspace, pure state estimation [pdf] [pdf]
- Lecture 3: Representation theory, density operators, partial trace [pdf] [pdf]
- Lecture 4: Mixed state entanglement, monogamy of entanglement [pdf] [pdf]
- Lecture 5: Shannon theory, data compression, spectrum estimation [pdf] [pdf]
- Lecture 6: Solution of the spectrum estimation problem [pdf] [pdf]
- Lecture 7: Schur-Weyl duality, quantum data compression, tomography [pdf] [pdf]
- Lecture 8: Compression and entanglement, entanglement transformations [pdf] [pdf]
- Lecture 9: Entanglement dilution, quantum teleportation, resource inequalities [pdf] [pdf]
- Lecture 10: Quantum circuits, swap test, quantum Schur transform [pdf] [pdf]
- Lectures 1-10 in a single file [pdf]