Exercise 2.8 Discussion

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 2.8}$

Alice is confused. She understands that $\ket 1$ and $-\ket 1$ represent the same state. But she does not understand why that does not imply that $\frac{1}{\sqrt 2}(\ket 0 + \ket 1)$ and $\frac{1}{\sqrt 2}(\ket 0 - \ket 1)$ would be the same state. Can you help her out?

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