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fix typo

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Zheyuan Wu
2026-03-26 00:02:26 -05:00
parent c8980a9611
commit b69f494648
2 changed files with 3 additions and 3 deletions
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presentation/ZheyuanWu_HonorThesis_Presentation.pdf
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presentation/ZheyuanWu_HonorThesis_Presentation.tex
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@@ -155,7 +155,7 @@
\end{block} \end{block}
\end{frame} \end{frame}
\input{./backgrounds.tex} % \input{./backgrounds.tex}
\begin{frame}{Information theory in classical systems} \begin{frame}{Information theory in classical systems}
@@ -187,7 +187,7 @@ This measures the intrinsic uncertainty of the quantum state and is basis-indepe
\begin{block}{Entanglement entropy} \begin{block}{Entanglement entropy}
For a bipartite pure state $|\Psi\rangle\in \mathcal{H}_A\otimes\mathcal{H}_B$, define the reduced state $\rho_A=\operatorname{Tr}_B\bigl(|\Psi\rangle\langle\Psi|\bigr).$ Its entanglement entropy is For a bipartite pure state $|\Psi\rangle\in \mathcal{H}_A\otimes\mathcal{H}_B$, define the reduced state $\rho_A=\operatorname{Tr}_B\bigl(|\Psi\rangle\langle\Psi|\bigr).$ Its entanglement entropy is
$$ $$
E(|\Psi\rangle)=S(\rho_A). E(|\Psi\rangle)=H(\rho_A).
$$ $$
Thus entanglement entropy is the von Neumann entropy of a subsystem, and it measures how entangled the bipartite pure state is. Thus entanglement entropy is the von Neumann entropy of a subsystem, and it measures how entangled the bipartite pure state is.
\end{block} \end{block}
@@ -272,7 +272,7 @@ Thus entanglement entropy is the von Neumann entropy of a subsystem, and it meas
$$ $$
\item A \textbf{mixed state} is represented by a density matrix \item A \textbf{mixed state} is represented by a density matrix
$$ $$
\rho=\sum_{j=1}^n p_j|\psi_j\rangle\langle\psi_j| \rho=\sum_{j=1}^n p_j|\psi_j\rangle\langle\psi_j|, \qquad \sum_{j=1}^n p_j=1, \qquad p_j\geq 0.
$$ $$
\item Pure states describe maximal information; mixed states describe probabilistic mixtures or partial information. \item Pure states describe maximal information; mixed states describe probabilistic mixtures or partial information.
\end{itemize} \end{itemize}