General Basis State Transformations

So far, we have used rather specific basis states. Let’s now write out a more general relationship. Suppose that Alice wants to use a basis labeled $A$, and I want to use one labeled $B$. The basis states are $|A_0⟩$ and $|A_1⟩$ for basis $A$ and $|B_0⟩$ and $|B_1⟩$ for basis $B$.