Math 401, Topic 6: Postulates of quantum theory and measurement operations
Section 1: Postulates of quantum theory
This part is a review of the quantum theory, I will keep the content brief.
If you are familiar with the linear algebra defined before, you can jump right into this section to keep your time as viewing those compact notations.
Pure states
Composite systems
Mixed states and density operators
Density operator of subsystems
State purification
Observables
Effects and Busch's theorem for effect operators
Measurements
Quantum operations and CPTP maps
Conditional operations
Section 2: Quantum entanglement
Bell states and the EPR phenomenon
Von Neumann entropy and maximally entangled states
Section 3: Information transmission by quantum systems
Transmission of classical information
Making use of entanglement and local operations
Superdense coding [very important]
Section 4: Quantum automorphisms and dynamics
