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forgot some modulus there

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Daniel Knüttel 2020-03-11 10:49:10 +01:00
parent bbbac43c82
commit 30f75f7bb2
1 changed files with 5 additions and 5 deletions
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10
thesis/chapters/stabilizer.tex
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@ -261,11 +261,11 @@ and $s=0$ are obtained with probability $\frac{1}{2}$ and after choosing a $j
\begin{equation}
\begin{aligned}
P(s=0) &= \hbox{Tr}\left(\frac{I + g_a}{2}\ket{\psi}\bra{\psi}\right) \\
&= \hbox{Tr}\left(\frac{I + g_a}{2}S^{(j)} \ket{\psi}\bra{\psi}\right)\\
&= \hbox{Tr}\left(S^{(j)}\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\\
&= \hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}S^{(j)}\right)\\
&= \hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\\
P(s=0) &= \left|\hbox{Tr}\left(\frac{I + g_a}{2}\ket{\psi}\bra{\psi}\right) \right|\\
&= \left|\hbox{Tr}\left(\frac{I + g_a}{2}S^{(j)} \ket{\psi}\bra{\psi}\right)\right|\\
&= \left|\hbox{Tr}\left(S^{(j)}\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\right|\\
&= \left|\hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}S^{(j)}\right)\right|\\
&= \left|\hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\right|\\
&= P(s=1)
\end{aligned}
\notag