General Formulation of Quantum Information
This course describes the general formulation of quantum information, where quantum states are represented by density matrices, changes in states are described by channels, and a more general class of measurements can be considered than was discussed in Basics of quantum information. The course also discusses mathematical ways of formalizing the distance or similarity between quantum states, and how they relate to channels and measurements in operational ways.
Lessons
- Introduction
- Pre-course Survey
- Basics
- Convex combinations of density matrices
- Bloch sphere
- Multiple systems and reduced states
- Introduction
- Basics of channels
- Channel representations
- Equivalence of the representations
- Introduction
- Mathematical formulations of measurements
- Naimark's theorem
- Quantum state discrimination and tomography
- Introduction
- Purifications
- Fidelity
- Post-course Survey
Helpful materials
Additional references
Alongside this course, you may find these resources to be helpful or interesting:
Michael Nielsen and Isaac Chuang. Quantum Computation and Quantum Information.
John Watrous. The Theory of Quantum Information.
Mark Wilde. Quantum Information Theory.
Presentation slides
Copies of the slides used to create the videos for this course are available for download in pdf format.