In the section of the course discussing computational basis, it gives an arbitrary example of ∣ϕ⟩ = 0.7 ∗ ∣0⟩ + 0.9 ∗ ∣1⟩.
However it later states that the sum of the squares of the probability amplitudes must total 1.
The probability amplitudes in the above example are 0.7 and 0.9, and 0.7^2 + 0.9^2 = 1.3.
Is this first example just incorrect / invalid?
Thanks
Ross
Hi @Ross_Deane, Thanks for reaching out to us.
None of the examples is incorrect. The probability amplitudes must always be equal to 1 as mentioned in the normalized property of the quantum state.
And the arbitrary state example ∣ϕ⟩ = 0.7 * |0> + 0.9* |1> in bra-ket notation represents the computational basis.
So, don’t confuse both of them these are two different concepts/representations.
Hope it will help, Happy Learning 