Ex5 2

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 5.2}$

For which sets of states is there a cloning operator? If the set has a cloning operator, give the operator. If not, explain your reasoning.

a) $\{ \ket 0, \ket 1 \}$,

b) $\{ \ket +, \ket - \}$,

c) $\{ \ket 0, \ket 1, \ket +, \ket - \}$,

d) $\{ \ket 0\ket +, \ket 0\ket -, \ket 1\ket +, \ket 1\ket - \}$,

e) $\{ a\ket 0 + b\ket 1 \}$, where $|a|^2 + |b|^2 = 1$.

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