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ObsidianVault/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md
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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]]