Exercise 2.7 Discussion

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 2.7}$

For each of the following states, describe all orthonormal bases that includes that state.

a) $\frac{1}{\sqrt 2}\left(\ket{0} + \i\ket 1 \right)$

b) $\frac{1 + \i}{2}\ket{0} - \frac{1 - \i}{2}\ket 1$

c) $\frac{1}{\sqrt 2}\left(\ket{0} + e^{\i\pi/6}\ket 1 \right)$

d) $\frac{1}{2}\ket{+} - \frac{\i\sqrt 3}{2}\ket{-}$