domain verification test

content/Math401/Math401_P1_2.md

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+# Math 401, Paper 1, Side note 2: Page's lemma
+
+The page's lemma is a fundamental result in quantum information theory that provides a lower bound on the probability of error in a quantum channel.
+
+## Statement
+
+Let $\mathcal{H}$ be a Hilbert space and $\mathcal{L}(\mathcal{H})$ be the set of linear operators on $\mathcal{H}$.
+
+Let $\mathcal{E}: \mathcal{L}(\mathcal{H}) \to \mathcal{L}(\mathcal{H})$ be a quantum channel.
+
+Then, for any $\rho \in \mathcal{L}(\mathcal{H})$, we have: