Exercise 2.3 Discussion

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 2.3}$

Which states are superpositions with respect to the standard basis, and which are not? For each state that is a superposition, give a basis with respect to which it is not a superposition.

a) $\ket +$

b) $\frac{1}{\sqrt 2}(\ket + + \ket -)$

c) $\frac{1}{\sqrt 2}(\ket + - \ket -)$

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

e) $\frac{1}{\sqrt 2}(\ket\i - \ket{-\i} )$

f) $\frac{1}{\sqrt 2}(\ket 0 - \ket 1)$