Ex7 2

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 7.2}$

Prove Equation 7.1:

(1)\begin{align} \sum_{x=0}^{2^n-1} (-1)^{x \cdot y} = \left\{\begin{array}{l}2^n \mbox{ if $y = 0$}\\ 0 \mbox{ otherwise.}\end{array}\right. \end{align}

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