2D subspace of a Hilbert space

[GwtBc]

Homework Statement

Have to read a paper and somewhere along the line it claims that for any distinct $\ket{\phi_{0}}$ and $\ket{\phi_{1}}$ we can choose a basis s.t. $\ket{\phi_{0}}= \cos\frac{\theta}{2}\ket{0} + \sin\frac{\theta}{2}\ket{1}, \hspace{0.5cm} \ket{\phi_{1}}= \cos\frac{\theta}{2}\ket{0} - \sin\frac{\theta}{2}\ket{1}$

where $$\theta$$ is between 0 and pi/2. Why pi/2? doesn't the upper bound have to be pi so that the inner product of the two can be anywhere between 1 and -1 (rather than between 1 and 0)

Homework Equations

The Attempt at a Solution

 

[Orodruin]

The values of the angle > pi/2 is just a reordering and rephasing of the values < pi/2.