fixed some minor issues
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@ -95,10 +95,10 @@ measuring a qbit is given by the following lemma:
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\begin{enumerate}
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\begin{enumerate}
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\item{If $J = \{\}$, one value is measured with probability $1$ and the stabilizers are unchanged.}
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\item{If $J = \{\}$, one value is measured with probability $1$ and the stabilizers are unchanged.}
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\item{If $J \neq \{\}$, $1$ and $0$ are measured with probability $\frac{1}{2}$ and the new state
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\item{If $J \neq \{\}$, $1$ and $0$ are measured with probability $\frac{1}{2}$ and after choosing
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$\ket{\psi'}$ is stabilized by
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a $j \in J$ the new state $\ket{\psi'}$ is stabilized by
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\begin{equation}
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\begin{equation}
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\langle \{(-1)^s g_a\} \cup \{K_G^{(i)} K_G^{(j)} | j \in J, i \in J \setminus \{j\} \} \cup \{K_G^{(i)} | i \in J^c\}\rangle
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\langle \{(-1)^s g_a\} \cup \{S_i S_j | i \in J \setminus \{j\} \} \cup \{S_i | i \in J^c\}\rangle
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\end{equation}}
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\end{equation}}
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\end{enumerate}
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\end{enumerate}
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\end{lemma}
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\end{lemma}
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