Observing = learning outcome

![[Pasted image 20260729093733.png]]

Because after observing all possibilities collapse to one.

Example:

![[Pasted image 20260729093827.png]]
![[Pasted image 20260729093834.png]]

The point here is that the result doesn't change if we observe at any point in the process!

##  Measuring a quantum system

Given a quantum state $\psi \in \mathbb{C}^n$ we will
![[Pasted image 20260729094624.png]]

BUT!!!
Measuring a quantum state CHANGES THE SYSTEM!!!

![[Pasted image 20260729094710.png]]
![[Pasted image 20260729094718.png]]