Vectors to describe quantum states can get tedious really quick, so we introduce a new notation.
We can rewrite a quantum state in the following way:
![[Pasted image 20260730101012.png]]

To represent the vector $e_i$ as its classical possibility we use $\ket{}$ .
For a classical possibility x, which is the i-th possibility represented by $e_i$ we use:
![[Pasted image 20260730101435.png]]