## 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]]