From b69f49464883e19717ebc6f0c1786b4efb462f90 Mon Sep 17 00:00:00 2001 From: Zheyuan Wu <60459821+Trance-0@users.noreply.github.com> Date: Thu, 26 Mar 2026 00:02:26 -0500 Subject: [PATCH] fix typo --- .../ZheyuanWu_HonorThesis_Presentation.pdf | Bin 860738 -> 837444 bytes .../ZheyuanWu_HonorThesis_Presentation.tex | 6 +++--- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/presentation/ZheyuanWu_HonorThesis_Presentation.pdf b/presentation/ZheyuanWu_HonorThesis_Presentation.pdf index 598e3a60f0733161974c3bc769536debe7e97979..42f22d752ac1e33829c15db70b10689f05543008 100644 GIT binary patch delta 117110 zcmX`SV|XTA6D=Iuwr$(ColNYB?K}2FcWm3XZA@(2nk19t%=4b}eSh}uu3h^_cVAsq zYt`C=!yLnL?DZEgh#9AtTZt)&pWsjgcpGV?{t)O*aIl1s2)zEdPKUnpMiXVgsU~)$ zDlkO3?wSQ(DT)vH*vQ)0rb`rPG(;t3@b`XZiVtGQHdP5=0~>l18u=^|QnnD{8M?O4 zIsl}|npp9l9is`1O&SsL%UOb$SIis$ZjhN7_n$i$H&-I61vo1=H!x9J7nB=VKw1`Y)54yIa5sZKEEZp$m z#t;31!b7nVJH*v+TegIg`(wI>LMYR66`YoCm$_m`~U}y@7Zw3S83=Ky7@EAz%+YBT%xr2jlmOoEsUd4IJXHFIT 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\input{./backgrounds.tex} \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} 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. \end{block} @@ -272,7 +272,7 @@ Thus entanglement entropy is the von Neumann entropy of a subsystem, and it meas $$ \item A \textbf{mixed state} is represented by a density matrix $$ - \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. \end{itemize}