Ex9 10

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 9.10}$

Suppose there is an error in the initial state, so that instead of starting with $\ket{00\dots 0}$, we run Grover's algorithm starting with the state

(1)\begin{align} \frac{1}{\sqrt{1 + \epsilon^2}} (\ket{00\dots 0} + \epsilon\ket{11\dots 1}). \end{align}

How does this error affect the results of Grover's algorithm?

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