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@@ -0,0 +1,27 @@
+## Classical possibilities
+finite
+all outcomes for a quantum system
+`Random bit generator with 1 bit output = classical possibilities 0 and 1`
+
+## Quantum States
+State of quantum system as vector
+-> each entry = classical possibility
+-> called amplitude
+-> can be negative and are complex numbers
+Amplitudes tell us the probability of quantum state being in the corresponding class. poss.
+probability = |amplitude|^2
+$Pr[x] = |\psi|^2$ 
+Also: $\sqrt{\sum^n_{i=1} |\psi|^2} = 1$  
+
+Example:
+![[Pasted image 20260729091741.png]]
+
+
+## Unitary transformation
+
+![[Pasted image 20260729092010.png]]
+
+Example with Pauli-matrices:
+![[Pasted image 20260729092121.png]]
+
+