This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2013.8.4) 28 JUN 2014 11:07 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **Densite.tex (./Densite.tex LaTeX2e <2011/06/27> Babel and hyphenation patterns for english, dumylang, nohyphenation, lo aded. ! Undefined control sequence. l.2 \graypar {Matrices densite} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2 \graypar{M atrices densite} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no M in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! ! Undefined control sequence. l.4 \graysec {Introduction du formalisme} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no I in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! ! Undefined control sequence. l.5 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (20.0pt too wide) in paragraph at lines 2--6 [] [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6 \item E tat pur : Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no E in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.7 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.8 \item $ |\Psi\p \text{ est un etat pur si } \hat{\rho} = |\Psi\p\q\Psi| $ Try typing to proceed. If that doesn't work, type X to quit. LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 8. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 8. ! Undefined control sequence. l.8 \item $ |\Psi\p \text{ est un etat pur si } \hat{\rho} = |\Psi\p\q\Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8 \item $ |\Psi\p \text { est un etat pur si } \hat{\rho} = |\Psi\p\q\Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8 ...{ est un etat pur si } \hat{\rho} = |\Psi\p \q\Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8 ...est un etat pur si } \hat{\rho} = |\Psi\p\q \Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (91.80527pt too wide) in paragraph at lines 8--9 \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 [][] = [] Overfull \hbox (21.11118pt too wide) in paragraph at lines 8--9 \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 \OMS/cmsy/m/n/10 j$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9 \item $ \hat{O} \text{ un observable : } \q\hat{O}\p=\text{Tr(}\hat{O}\h... Try typing to proceed. If that doesn't work, type X to quit. ! Undefined control sequence. l.9 \item $ \hat{O} \text { un observable : } \q\hat{O}\p=\text{Tr(}\hat{O}\h... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9 \item $ \hat{O} \text{ un observable : } \q \hat{O}\p=\text{Tr(}\hat{O}\h... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9 ...hat{O} \text{ un observable : } \q\hat{O}\p =\text{Tr(}\hat{O}\hat{\rh... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9 ... \text{ un observable : } \q\hat{O}\p=\text {Tr(}\hat{O}\hat{\rho}\tex... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9 ...q\hat{O}\p=\text{Tr(}\hat{O}\hat{\rho}\text {)} $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (89.54144pt too wide) in paragraph at lines 9--11 [][][] \OT1/cmr/m/n/10 = [] Overfull \hbox (32.87552pt too wide) in paragraph at lines 9--11 [][][][]$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.11 \item 2 sous-systemes A et B de bases $\{|j\p\}$ et $\{|\mu\p\}$: Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no 2 in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no A in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no B in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! ! Undefined control sequence. l.11 \item 2 sous-systemes A et B de bases $\{|j\p \}$ et $\{|\mu\p\}$: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! ! Undefined control sequence. l.11 ...es A et B de bases $\{|j\p\}$ et $\{|\mu\p \}$: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no : in font nullfont! ! Undefined control sequence. l.12 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (17.4683pt too wide) in paragraph at lines 11--13 \OMS/cmsy/m/n/10 fj\OML/cmm/m/it/10 j\OMS/cmsy/m/n/10 g$ [] Overfull \hbox (18.8033pt too wide) in paragraph at lines 11--13 \OMS/cmsy/m/n/10 fj\OML/cmm/m/it/10 ^^V\OMS/cmsy/m/n/10 g$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.13 \item $ |\Psi\p \text{ est un etat pur si } \hat{\rho} = |\Psi\p\q\Psi| $ Try typing to proceed. If that doesn't work, type X to quit. ! Undefined control sequence. l.13 \item $ |\Psi\p \text{ est un etat pur si } \hat{\rho} = |\Psi\p\q\Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.13 \item $ |\Psi\p \text { est un etat pur si } \hat{\rho} = |\Psi\p\q\Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.13 ... est un etat pur si } \hat{\rho} = |\Psi\p \q\Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.13 ...st un etat pur si } \hat{\rho} = |\Psi\p\q \Psi| $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (91.80527pt too wide) in paragraph at lines 13--14 \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 [][] = [] Overfull \hbox (21.11118pt too wide) in paragraph at lines 13--14 \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 \OMS/cmsy/m/n/10 j$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.14 \item $ \hat{O} \text{ une observable de A, sa valeur moyenne est : } \... Try typing to proceed. If that doesn't work, type X to quit. ! Undefined control sequence. l.14 \item $ \hat{O} \text { une observable de A, sa valeur moyenne est : } \... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...ervable de A, sa valeur moyenne est : } \q \hat{O}\otimes \hat{I}_B\p... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...yenne est : } \q\hat{O}\otimes \hat{I}_B\p =\text{Tr(}\hat{O}\hat{\rh... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...est : } \q\hat{O}\otimes \hat{I}_B\p=\text {Tr(}\hat{O}\hat{\rho}\tex... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...at{I}_B\p=\text{Tr(}\hat{O}\hat{\rho}\text {)} = \sum_{i,j}\rho_{ij}M... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...\text{)} = \sum_{i,j}\rho_{ij}M_{ij} \text { avec } \rho_{ij}=\sum_{\... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ..._{ij} \text{ avec } \rho_{ij}=\sum_{\mu}\q i\mu|\psi\p\q\psi|j\mu\p$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ... avec } \rho_{ij}=\sum_{\mu}\q i\mu|\psi\p \q\psi|j\mu\p$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...vec } \rho_{ij}=\sum_{\mu}\q i\mu|\psi\p\q \psi|j\mu\p$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.14 ...{ij}=\sum_{\mu}\q i\mu|\psi\p\q\psi|j\mu\p $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (205.2027pt too wide) in paragraph at lines 14--15 [][][] \OMS/cmsy/m/n/10 [] Overfull \hbox (21.83435pt too wide) in paragraph at lines 14--15 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (43.43103pt too wide) in paragraph at lines 14--15 [][][][] \OT1/cmr/m/n/10 = [] Overfull \hbox (92.84154pt too wide) in paragraph at lines 14--15 [][] \OML/cmm/m/it/10 ^^Z[]M[][]^^Z[] \OT1/cmr/m/n/10 = [] Overfull \hbox (57.07208pt too wide) in paragraph at lines 14--15 [][] \OML/cmm/m/it/10 i^^V\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 j^^V$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.15 \item T race partielle : $\hat{\rho}_A = \text{Tr}_B\text{(}\hat{\rho}\t... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no T in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.15 \item Trace partielle : $\hat{\rho}_A = \text {Tr}_B\text{(}\hat{\rho}\t... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...rtielle : $\hat{\rho}_A = \text{Tr}_B\text {(}\hat{\rho}\text{)}=\sum... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...ho}_A = \text{Tr}_B\text{(}\hat{\rho}\text {)}=\sum_j\q j|\hat{\rho}|... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...t{Tr}_B\text{(}\hat{\rho}\text{)}=\sum_j\q j|\hat{\rho}|j\p$ avec $\... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...at{\rho}\text{)}=\sum_j\q j|\hat{\rho}|j\p $ avec $\{|j\p\}$ base de ... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no a in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! ! Undefined control sequence. l.15 ...)}=\sum_j\q j|\hat{\rho}|j\p$ avec $\{|j\p \}$ base de B ou encore $\... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no b in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no B in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! ! Undefined control sequence. l.15 ...um_{i,j}\alpha_{i\mu}\alpha^{*}_{j\mu}|i\p \q j|$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ..._{i,j}\alpha_{i\mu}\alpha^{*}_{j\mu}|i\p\q j|$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.16 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.17 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.19 \graysec {Proprietes} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no P in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! ! Undefined control sequence. l.20 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (22.23958pt too wide) in paragraph at lines 15--21 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (42.40848pt too wide) in paragraph at lines 15--21 [][][][][] \OT1/cmr/m/n/10 = [] Overfull \hbox (36.54248pt too wide) in paragraph at lines 15--21 [][] \OML/cmm/m/it/10 j\OMS/cmsy/m/n/10 j[]j\OML/cmm/m/it/10 j$ [] Overfull \hbox (17.4683pt too wide) in paragraph at lines 15--21 \OMS/cmsy/m/n/10 fj\OML/cmm/m/it/10 j\OMS/cmsy/m/n/10 g$ [] Overfull \hbox (22.23958pt too wide) in paragraph at lines 15--21 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (82.97731pt too wide) in paragraph at lines 15--21 [][] [][] \OML/cmm/m/it/10 [] []\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ij\OMS/cmsy /m/n/10 j$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.21 \item T race : Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no T in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.22 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.23 \item $ \hat{\rho}_A^{\dagger}=\hat{\rho}_A$ (on peut diagonaliser) Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no ( in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no ) in font nullfont! Overfull \hbox (22.23958pt too wide) in paragraph at lines 23--24 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (11.68407pt too wide) in paragraph at lines 23--24 []$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.24 \item T r$\left(\hat{\rho}_A\right)=1$ Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no T in font nullfont! Missing character: There is no r in font nullfont! Overfull \hbox (30.01738pt too wide) in paragraph at lines 24--25 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 24--25 \OT1/cmr/m/n/10 1$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.25 \item $ \hat{\rho}_A$ definie positive : $\q\phi|\hat{\rho}_A|\phi\p>0$ Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. \q l.25 \item $\hat{\rho}_A$ definie positive : $\q \phi|\hat{\rho}_A|\phi\p>0$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.25 ...nie positive : $\q\phi|\hat{\rho}_A|\phi\p >0$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.26 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (11.68407pt too wide) in paragraph at lines 25--27 []$ [] Overfull \hbox (39.71184pt too wide) in paragraph at lines 25--27 \OML/cmm/m/it/10 ^^^\OMS/cmsy/m/n/10 j[]j\OML/cmm/m/it/10 ^^^ > [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 25--27 \OT1/cmr/m/n/10 0$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.27 \item E tat pur : $\hat{\rho}^2=\hat{\rho}$ donc $\text{Tr}\left(\hat{\r... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no E in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! ! Undefined control sequence. \text l.27 ...ur : $\hat{\rho}^2=\hat{\rho}$ donc $\text {Tr}\left(\hat{\rho}^2\rig... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.27 ... $\text{Tr}\left(\hat{\rho}^2\right)=\text {Tr}\left(\hat{\rho}\right... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (20.21179pt too wide) in paragraph at lines 27--28 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (5.17015pt too wide) in paragraph at lines 27--28 []$ [] Overfull \hbox (43.06715pt too wide) in paragraph at lines 27--28 [] [] \OT1/cmr/m/n/10 = [] Overfull \hbox (37.19211pt too wide) in paragraph at lines 27--28 [] [] \OT1/cmr/m/n/10 = [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 27--28 \OT1/cmr/m/n/10 1$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.28 \item E tat "de melange statistique" : $\hat{\rho}^2=\hat{\rho}$ donc $\... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no E in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no " in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no " in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! ! Undefined control sequence. \text l.28 ...e" : $\hat{\rho}^2=\hat{\rho}$ donc $\text {Tr}\left(\hat{\rho}^2\rig... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.28 ... $\text{Tr}\left(\hat{\rho}^2\right)<\text {Tr}\left(\hat{\rho}\right)$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.29 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.31 \graysec {Evolution temporelle} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no E in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! ! Undefined control sequence. l.32 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (20.21179pt too wide) in paragraph at lines 28--33 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (5.17015pt too wide) in paragraph at lines 28--33 []$ [] Overfull \hbox (43.06715pt too wide) in paragraph at lines 28--33 [] [] \OML/cmm/m/it/10 < [] Overfull \hbox (26.6366pt too wide) in paragraph at lines 28--33 [] []$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.33 \item $ i\hbar\frac{\partial\hat{\rho}}{\partial t}=-[\hat{\rho},\hat{H}]$ Try typing to proceed. If that doesn't work, type X to quit. ! Undefined control sequence. l.34 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.35 \graysec {Trace partielle} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no T in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! ! Undefined control sequence. l.36 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (31.01237pt too wide) in paragraph at lines 33--37 \OML/cmm/m/it/10 i[][] \OT1/cmr/m/n/10 = [] Overfull \hbox (32.0729pt too wide) in paragraph at lines 33--37 \OMS/cmsy/m/n/10 ^^@\OT1/cmr/m/n/10 [[]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 ]$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.37 \item S upposons qu'il y a 2 sous-systèmes A et B tq $|\psi \p = |\phi_... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no S in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no ' in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no 2 in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no - in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no ¨ in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no A in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no B in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no q in font nullfont! ! Undefined control sequence. l.37 ...l y a 2 sous-systèmes A et B tq $|\psi \p = |\phi_A\p \otimes |\phi... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.37 ...-systèmes A et B tq $|\psi \p = |\phi_A\p \otimes |\phi_B\p$. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.37 ...tq $|\psi \p = |\phi_A\p \otimes |\phi_B\p $. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no . in font nullfont! Overfull \hbox (20.206pt too wide) in paragraph at lines 37--38 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 \OT1/cmr/m/n/10 = [] Overfull \hbox (23.02785pt too wide) in paragraph at lines 37--38 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ^^^[] \OMS/cmsy/m/n/10 [] Overfull \hbox (15.61913pt too wide) in paragraph at lines 37--38 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ^^^[]$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.38 \item M atrice densité : $\hat{\rho} = |\psi\p \q\psi| = \ldots = (|\ph... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no M in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.38 ...m Matrice densité : $\hat{\rho} = |\psi\p \q\psi| = \ldots = (|\phi... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.38 ...atrice densité : $\hat{\rho} = |\psi\p \q \psi| = \ldots = (|\phi_A\... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.38 ...o} = |\psi\p \q\psi| = \ldots = (|\phi_A\p \q\phi_A|)\otimes|\phi_B\p... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.38 ... = |\psi\p \q\psi| = \ldots = (|\phi_A\p\q \phi_A|)\otimes|\phi_B\p\q... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.38 ...ots = (|\phi_A\p\q\phi_A|)\otimes|\phi_B\p \q\phi_B|)$ \, \, $\Righta... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.38 ...s = (|\phi_A\p\q\phi_A|)\otimes|\phi_B\p\q \phi_B|)$ \, \, $\Rightarr... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (15.72566pt too wide) in paragraph at lines 38--39 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (29.85648pt too wide) in paragraph at lines 38--39 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 \OMS/cmsy/m/n/10 j \OT1/cmr/m/n/10 = [] Overfull \hbox (22.22212pt too wide) in paragraph at lines 38--39 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (46.0557pt too wide) in paragraph at lines 38--39 \OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ^^^[]^^^[]\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 [] Overfull \hbox (35.12715pt too wide) in paragraph at lines 38--39 \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ^^^[]^^^[]\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 )$ [] Overfull \hbox (10.00002pt too wide) in paragraph at lines 38--39 \OMS/cmsy/m/n/10 )$ [] Overfull \hbox (15.72566pt too wide) in paragraph at lines 38--39 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (19.46187pt too wide) in paragraph at lines 38--39 [] \OMS/cmsy/m/n/10 [] Overfull \hbox (12.05315pt too wide) in paragraph at lines 38--39 []$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.39 \item O n définit : $\hat{\rho}_A = Tr_B(\hat{\rho})$ et $\hat{\rho}_B ... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no O in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no : in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Overfull \hbox (22.23958pt too wide) in paragraph at lines 39--40 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (31.57518pt too wide) in paragraph at lines 39--40 \OML/cmm/m/it/10 Tr[]\OT1/cmr/m/n/10 ([])$ [] Overfull \hbox (22.60866pt too wide) in paragraph at lines 39--40 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (31.2061pt too wide) in paragraph at lines 39--40 \OML/cmm/m/it/10 Tr[]\OT1/cmr/m/n/10 ([])$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.40 \item A fin de calculer plus simplement, on utilise la base suivante : $... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no A in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.40 ...n utilise la base suivante : $\{ |0_A0_B\p , |0_A1_B\p, |1_A0_B\p, |1... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.40 ...a base suivante : $\{ |0_A0_B\p, |0_A1_B\p , |1_A0_B\p, |1_A1_B\p\}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.40 ...ante : $\{ |0_A0_B\p, |0_A1_B\p, |1_A0_B\p , |1_A1_B\p\}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.40 ...|0_A0_B\p, |0_A1_B\p, |1_A0_B\p, |1_A1_B\p \}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (128.03218pt too wide) in paragraph at lines 40--41 \OMS/cmsy/m/n/10 fj\OT1/cmr/m/n/10 0[]0[]\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 j\ OT1/cmr/m/n/10 0[]1[]\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 1[]0[ ]\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 1[]1[]\OMS/cmsy/m/n/10 g$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.41 \item O n peut réécrire la trace partielle pour trouver $\hat{\rho}_A$... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no O in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.42 $\hat{\rho}_A = Tr_B(\rho) = \sum_{j=0,1} \q j_B |\hat{\rho}|j_B\p = \q... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.42 ...o) = \sum_{j=0,1} \q j_B |\hat{\rho}|j_B\p = \q 0_B|\hat{\rho}|0_B\p... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.42 ...\sum_{j=0,1} \q j_B |\hat{\rho}|j_B\p = \q 0_B|\hat{\rho}|0_B\p + \q... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.42 ...\hat{\rho}|j_B\p = \q 0_B|\hat{\rho}|0_B\p + \q 1_B|\hat{\rho}|1_B\p$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.42 ...\rho}|j_B\p = \q 0_B|\hat{\rho}|0_B\p + \q 1_B|\hat{\rho}|1_B\p$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.42 ...\hat{\rho}|0_B\p + \q 1_B|\hat{\rho}|1_B\p $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (11.68407pt too wide) in paragraph at lines 41--43 []$ [] Overfull \hbox (22.23958pt too wide) in paragraph at lines 41--43 [] \OT1/cmr/m/n/10 = [] Overfull \hbox (42.13069pt too wide) in paragraph at lines 41--43 \OML/cmm/m/it/10 Tr[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ^^Z\OT1/cmr/m/n/10 ) = [] Overfull \hbox (76.20529pt too wide) in paragraph at lines 41--43 [][] \OML/cmm/m/it/10 j[]\OMS/cmsy/m/n/10 j[]j\OML/cmm/m/it/10 j[] \OT1/cmr/m/n /10 = [] Overfull \hbox (42.26955pt too wide) in paragraph at lines 41--43 \OT1/cmr/m/n/10 0[]\OMS/cmsy/m/n/10 j[]j\OT1/cmr/m/n/10 0[] + [] Overfull \hbox (34.49174pt too wide) in paragraph at lines 41--43 \OT1/cmr/m/n/10 1[]\OMS/cmsy/m/n/10 j[]j\OT1/cmr/m/n/10 1[]$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.43 \item E n image, cela donne : Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no E in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.44 \squishlist The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.45 \item $ \hat{\rho}_A$ : Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no : in font nullfont! Overfull \hbox (11.68407pt too wide) in paragraph at lines 45--46 []$ [] ! Undefined control sequence. l.47 \includegraphics [width = 3cm]{fonctions/TrB.png} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no [ in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no = in font nullfont! Missing character: There is no 3 in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no ] in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no / in font nullfont! Missing character: There is no T in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no B in font nullfont! Missing character: There is no . in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.49 \item $ \hat{\rho}_B$ : Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no : in font nullfont! Overfull \hbox (12.05315pt too wide) in paragraph at lines 49--50 []$ [] ! Undefined control sequence. l.51 \includegraphics [width = 3cm]{fonctions/TrA.png} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no [ in font nullfont! Missing character: There is no w in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no = in font nullfont! Missing character: There is no 3 in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no ] in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no / in font nullfont! Missing character: There is no T in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no A in font nullfont! Missing character: There is no . in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no g in font nullfont! ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.53 \item I l faut sommer les éléments entourés en pointillés et les pla... Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no I in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no © in font nullfont! Missing character: There is no à in font nullfont! Missing character: There is no   in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no ' in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no . in font nullfont! ! Undefined control sequence. l.54 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.55 \squishend The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ) ! Emergency stop. <*> Densite.tex *** (job aborted, no legal \end found) Here is how much of TeX's memory you used: 8 strings out of 495059 165 string characters out of 3182031 52057 words of memory out of 3000000 3291 multiletter control sequences out of 15000+200000 3640 words of font info for 14 fonts, out of 3000000 for 9000 14 hyphenation exceptions out of 8191 18i,3n,12p,239b,59s stack positions out of 5000i,500n,10000p,200000b,50000s ! ==> Fatal error occurred, no output PDF file produced!