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 # 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
+