From c68fb8cd1d5b58205ff560fe9c94d1c3dcdac3ee Mon Sep 17 00:00:00 2001 From: Benjamin Neumann Date: Wed, 29 Jul 2026 22:14:33 +0200 Subject: [PATCH] vault backup: 2026-07-29 22:14:33 --- .obsidian/workspace.json | 2 +- .../Anhänge/Pasted image 20260729220918.png | Bin 0 -> 32868 bytes .../6. Composite Systems/Composite Systems.md | 16 ++++++++++++++++ 3 files changed, 17 insertions(+), 1 deletion(-) create mode 100644 SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729220918.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 6d7a1d8..b025834 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -216,6 +216,7 @@ }, "active": "25f5b25d5eca7203", "lastOpenFiles": [ + "SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729220918.png", "SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729215837.png", "SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729215759.png", "SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729215146.png", @@ -231,7 +232,6 @@ "SS2026/Quantum Computing/5. Partial observing and measuring/Anhänge/Pasted image 20260729123015.png", "SS2026/Quantum Computing/5. Partial observing and measuring/Anhänge/Pasted image 20260729122952.png", "SS2026/Quantum Computing/5. Partial observing and measuring/Anhänge/Pasted image 20260729122833.png", - "SS2026/Quantum Computing/5. Partial observing and measuring/Anhänge/Pasted image 20260729122658.png", "SS2026/Quantum Computing/5. Partial observing and measuring/Anhänge", "SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md", "SS2026/Quantum Computing/5. Partial observing and measuring", diff --git a/SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729220918.png b/SS2026/Quantum Computing/6. Composite Systems/Anhänge/Pasted image 20260729220918.png new file mode 100644 index 0000000000000000000000000000000000000000..484401b77f7247797938788c3b2746eba81854ca GIT binary patch literal 32868 zcmbrlWmH^2+bu|fyL)gaxVyV+g1fuB1a}Ya4FuQV8r-3Af;)}7+jQRVTX*iAxj*ij z`O&LapFUEjs-CCzv-hqj6(wn81OfyI2nb|Z83{EAh|l5>5TCxl!GMnpz}HcNzdpID zNsB?$Ono^5|A4X-RTPDQs82wAHHHTNhIf+Dc7=dI>HqinH0)Sr20n=4CaLA7?r7oW zY3yPSA?;#r?%-o6l7&`yC}iT5SjCF3 z0El<{n&mdW4)yBS3;8S>P8TjxX+77O?Rvpj{(hYBF&ICEIB+AuB-`S!-u|F}nByA{ z6K;$bZk)j@71Q0zg4EA~#I9V2X97NiXHgRsRrs;@cJX+-`O5sdgWK~s$Q*DLV;DGp zBK$i1!Ab86MaC)tE9n37fnD2(`k$-&*QEVIlz%4TJx_0Ze1w}s{<}Ngf%0z8Yv6ly zcPc|TsOR5P`dI=A7{dSk7oKUWg~a-wColbvCmXX4{5xktum8X9kkJ-Ci1we$T#;kQ z{?p_G0vz#)^}|LK%irM+epMTYe5=qJ-O`)pcn9x0g>PeGM`a{$kgmFZjD?rKaQz=< z*D~;q&-tD52uG|4I2a*!+aN6~;~j4Q2#59JXX(ORS8`2I5ltoG3X-E={EnNz#I>9e zo`{W@3V_~EN6ASy*Vy=`TC#M4k;4ePu$$d!ebgdPYsO*5rGqE&;fLLclhcI2H|Ku1 zz84Ym8e?&*KXeEPQTrC+`sGcWZ)1~@!w|c`njrQJCM!abL%6Mu_=JUvU~W?xm$;o| zoaMXXvZIaFDKCp*E6C4PRg0krQ}F#4k7NHjOM$g_t1uuCiB069mb${0qxN9i&nnur z)B~6Jz^LoQVD8N`+l-UT0a+cIMkVA6?)UT0_sj!*_bC1=U!OTqrqH3+vJfPLTG@1>@$Z zC|9~{thDZbz5g5jD;-G8?Fep$z+8bjg~_DtpLq@};i<(0@n?4|PRR2*VaKh!ZYC4^ zF2PO;!lyeJroZD$5+rw}1hJk=zg_fFj}8e&tAsIWjMWhWx>~c4sy1xc~vnhh#CczC) z>-gr0#^~{se)glTgD-@{o+F{d=BkJ$#w$=?_?ExLA9cdT0W!zm8gTdEet-KjXGwMb zcVBSMX7(AARksWpl-!8ID^o2rf2HWA1}Y1g*`~gZhFxP;0ynV%_sF! z__hoVEm+9ggi00?`fY$UaEadPRC~wkYUA_M1R-sbZ6tNXTX$o7RZ@u*QBii83PTX{ z4^X*tW%v-+(;=r-rMva|qwagnhlXTG0R3DS+qkU`&hzf)Q(S0}HssVHd_F~uHc}LP z@EWU|qIF-aU+u$WSd+=;y{9W z$;6gy$3vS|Mf^+QUPSKW9;#suGvkg+VdTCZ$jIbyZ&jtL@E2ccih9mMhMG9-k@iTY zq1}m~qjQ<6K1^MfI{~GAYvKH7f?w?W5Vkixr?cli32G2u6QrGZHA5kzXiB zw49TA7ll9nO1STzReD_pGyDT|_<3T9Q)AKXiIm+VR;JjOR5OTQz~ znzj>wR~+vJ_r+H^CSsXQfuQvE@36Vskp4po{b}y(rO=g7CfQ8dt3ENGFV2L07PlSN zrknceF^R4h(-NHjU&(|G68@gMnPm>uXCT&+)Ai1p_`WC#)yJn5OCA^-r$q$X#C=ep zU9WbFkJAoNs`rFB43nbya zsO|s^)`I%cR%t}v|8)UiN4eOM|FEMYV9_{SLJ0$sW0696 z)KHH0{2sUlEaqJH1M{8?m%mT#D!zJa{^RIO#cQ(+!Au_`1LZfk`5|&lr z)1E3cAB;^?>wdEkzgw`yZ)B)RXiYCyjxKwX#K~beowhkxfm2$W&CT=vWuk21^b*-- z*DK2Z47*R=^K;}Te=*{-?V2F+tuT(X=~18fn|4-e9BBMy4^hym;w3adS+JEVFnv?l z-C1x|m!NS!>kCPJb9e$#JMV*_m+1lb)t{zs5z=XWO>{esv^X3daTr5?LJ;07(H8RBvYtRy54Wq8F2dcN=ILDaE@rSobJ zGcJ71!;%Mr?$VB@jf!#0l*iYSau|`$nIPK#Q3vCSbVv$%|GT-yCg;o>?{kgWNHT`? zG&5?R^dU$%vwTa*xC!si3$F-`6(26<0d4&Fi7yX@?WRiP;5x=mJ2Fkj)`L8Vj`GVK zSx-x8D3yPTmKBLao>3VpwZ17?jgPTmJBZ&9I1Uf&>E2x>5auRd47kd+6uX40tPtL| zo(WTgw_leyvd7;)qqi}%8pX{=`}EuwT&F2+xzm&ie4MD^a~a-UWm9NBOu>1?3SA(# z`IM=K6nRxya$#_CmR0snBR^M!tSmX7r2|`|2HmJ)KVeW3>jxr42C5`)6Oy&0VR3gm z!GGA#>PZ1#@gi}vIJlo(=bfg~-gc*PO{TIqgiG$f`_*LHJG76ji5;T%)THk}L>Ar< zAczT+5t2PWK(H3Nikry5h>p_~3hBe62eOCZUDIrZ-a`!nw=78vZo8GN4$*YV0;Ggl zVCtRXtJKK`%+N9-7a;BilVXuGj1Gt~yy)BT{@lPMEq}%^z+cXP+4+UCiKi}hcDL>? zIzLygr6;jDL&@=jCLR%XKPqfn6HK@Jy%_HEhk+ko?{yiJ&kiP)-~!X| zSc=yPN;sL->$baehhVcpw2u+`6b;awO^bKGfGCNmNZ8BTUFX8g>j*7gl0V zW$Carx6lhr?2zWt6+BgHI8j1>a@Z;>%cJaRdkuWjQeg^Xg%vrD8T?c9Lg_EA$K zw>N)hh6B;|^gwSs;3I0R@Frlns0W%sx7=0x51a7iyyehToQnftv%a4Y>DJ=@xjcqb z`FD=$9uwEeP;U;8SL_2EK2$?H1IQNUa3%o`?uLH*&UbYkr{rJNG0*K9gWw^gFp+s$ zfz++pS6{?3ky%4CQzXbWomb>~t@)9uod{HlYTN@_V$hsINstsP5WA2OL0?9%Nom{S zZ4v#(iw%RS%ISQ*P&7tB_RoW%ReUz2X8{Se%YI;c1wX9N_TQ9H7s z&)pRSF9xV8)sc}ER?&74aV(}uQ(#HM#V&YUKk$O z>Ok~;_@KgV_#?Qo>Z$VPL9Y+RPoXNv+o}PrD80kJcmMq7n{{o(qA_7t@fAaj`~2j7 z;hP$aa*P(w4j^I57;`=2MM`m5wPmdU)^qZUf57JeH0Ion)>6>Xdo4n=*yF4}n+{&l z8$+$Td-sRhhJ3s-#$n%px$%HB<;@K z3Gdv^lX6+o;mH*Hq7SkcqGhD`Jshw;n^E!%9=>r(Yv)#M64U`6#DC1cM^AEM9?UFX zRpc|VwgB}w7sL;Kg3Dn!rFN^n%XQ`c_y?f3V?WRxZ~Du!EljNY_W=bJh^9Lpiuh@P zW)(q)!fwrxYC`qKn%w9(UVx5?qVhVM7ZoMY6@~jKWMj^Zf&N{ z)s=g(HkqixGPdW~1IU`V(=nSkA3GBL^w8xYgxE-LcVBw++);v@ zRMzCt?RCa34HR=0WK&rd!prRQ4dhhOF7f4obZrTn5{A5${81flN4snQlfY$=>@?Qr zQ>u58uebb_7q8NsBM?ezvSr2}mvEiDtOqWH3k%qG&R2(_cxB4t_(z8U&|nzer5|20 z$Egz2=>^0eWKh#n;98!>)z>J`e<<4=b4t6R6>3tEMSRBz>VLODhunu0{%eB2sE)ZW z-Xkm>srAJNn6nd9@j{KdD~UfvJ=ukMe)Pvr%-?XuY3rR+sZX}u@n*zvUIj6Jyzv5I zits|-$>Ui3!Kbylm-p8v&y@2g4-tr86ON@!(aPgiU$_SJ^fH$Np7TP93WHcxkU~8p zl{=Y9Uw(crW@KGD%u}iB%tFm%xzvcqj5$C9Y#5z$@SQV}K% z%-v8jyGDd1)EK6VTZ4Ikk@HP8$K-HZi#E+6dG!?a*UL(*He}|w2u?W^D~E(m6@ba* zz@orQU|re8PZ7*hofDf;$G4$eklTDNUjGItmf-pc$oGhiRA^Gy3d`VG=MEc9n}JV6 z9PGTVsrQXu`cc%(!T#OSui4ZE5@wezlQ3lGIZeu#cnLa&>;Oef$isE#+jNJ>h5n~7 zd))m6@|=Ro9p$p}dwyO=K!fk#>23&NQ-T9jPGq$X=5Ua90U9C>TXV?|&6lv2YP?qj!Bl0(zS( zr2`)^{!b{kNyZp51d(h#G^R`xIaJH4AwNl&KyH;^l+MRT8hPqR>0Vr*anYv1>$*H#mB=(JIJQ@PO!p@A{udqTD2x~>dF%;H__scmiC5_4j;4W<0Rb+ zseIm%ifrMn|2AumzA$CaqYU}CQXP%%j^ZghSq@t-%1}`YF(syCg9`ArgInAvw3*Is zgm+M}R)fdako52sep=?io!DCQmt(wB$z{hVhdmPRJ7%OwkUi!?W$qv%I3?eV_I?-&s1PVF;h!|p=OJzan`TDB3abt;K z4wYmr2d^Dec)u3Z1n7OG#N9r(71ts+o6J#N&(mNMaJ#p|T4KbyCC@qgjG!CvR}p6Y&5OIWtuUWZlv7U1a->$Jr$}*19Ockd7x&PDlg&t(&xhQJK}@*8p<^ z&;7|%wiEH8Q5Rj|Woz(MhJzC2q6M7@MkU8|ECVs`x@Q<-1cDee*<|sjQ}UFpnze3rtzV#1(8E*T&koEB3X|go4Pr^2AS58; z1;{g2F)v>$d;Yq7bK`E0Z9C1GWzNEv z8ba0E*|0liQ&^x83i2 z(FZWi*DymWY`2W1LY(>)LcgvaQ^8UqypgwO&bqgrb((Iv5N*_>vUur^cyK8|^)_vu zF+JuYAVl284NIe`HC<`tM_+j97hGn6ccA2IYEss50dQ5qf#3H<9YmZlQNXm~1GAy3 z<}bBWcw=4E(Z);(^;RnD$#yWmD$o~JE=|d0WUy6VVyJt-MXbv)pyx2WhMx|DcArl% zb*F_|M;SD#rdcfPzE3G&{jGDK3jt9Em`ctdNf5if0pfq{iJ>1Nh#p&EdDM||?npTf zFI1TM8ym&PNUcHSUHD@q;ge3bwprdn>PVtP`%ZU6Z&27y1XqPTK?9+p*R7{!iFRHg zR%f64E~gRGBVvl1W$d%@?P|jwL|f53=KBLeH1ld%53oS693UNst2qD(m}yCamb8fc zq(g{r^*34XH54@YCyy?kvTzcMxfs7J09TOt*_^h{;?&pL9U*596+_4S=bOgeeCK-*$RJlVuG;Q#YDH}I^Y7c#nuws|78r)j&vegf@Nmb{2pb=jP^KMmL*ew_ zcqchk&QeoLeN7aKJA5&Rx_C(3r~L{q?x+3taPEf*-&TcNwgfRx)2Et)X49ocs_Ckh zQRS@WV3`Hx^Rf4}q)}60=?~6}k^Hr=bBr@yM&hE##FSobuK62`A2EsGi<+DlF^}YE zD@sie(C!iU6r+>SFxM}wzYj`$89DO5oWopju-;BxM11!BBcT*Ce0jv%omfJ)Qfv)u zfNnK0A(=jFX6;QS-wE?uQsg<1VL-`3aqWn{uEeMy85&dq1{aXw>euyrPn>fxAxo9% zrCoU%4|!leZKkN_()kGsCjScv8m2Dn24CJf> z=G&qhnnLQ~Vk!yI!|xJWs+wLHIBxn~ICA*z>of+C3kHTGG_5Y;lySbAH1q+}Dm|5~ zxhxw4;NFJ2k9o}7#b7%Yh(P5_u-7n1RSh@+JhgljQw$Pnf1l)@tY3;U&ghtqizZ_| zqCHWvW#gnmc7o-$A3#z`6Wa^5=} z2U@3*oh!>ft2MRk3OC(&>#O3mbx$c8=AG3n$uwgNtJSB%Fk`eRTykSM<-^T=PoSf6 z0|zoXQ@&Sc*m5rB+A(veoXD53&*`!%NrNS*7c|;v<#CW+o2yPszl#RhjiB+ph++B` z_!=r6(}FjcQ6Y8ELKb6w_%6I0MFkLPkHcJh7Dd`-b*(sbSYHY!XIC-9+B=KIeCgV>b2rDFvSP#|>h_LbqF$4dp*sk(OROAEigjPoqOSWsryuL$URU_rD zDXH5(b?Pd;;s2*>>ZmaR0M7AsT4hfC%l|AtMt%gZG*bj7tVkUy*`qJQVIbhz z|D-`a5L~Oc5{GNbzsFsMJdR-ClB=O4z{SQ{Q?zvdowtVuA$291r1L@j={ z$^T0G7%ZwiltrR&MYLm}xjS~Dyc@U4>@qQOk=FC|BVR&8Ra<=bko}$D5l59Zc@PgD zcS0y&4Yo(VojYWg@$qkOQk=qKa?OHOkHjji#CH`mU#lMaLT9G1QpdJm7d=_fNyZtQ zli>NCrEzlNjYo)c-5xilOL(817K@2~JEK(uu@y?=gw0@Wp9Lh*rWIuD<1K~@g3r-N z3N-tlN*M#u2n+42V(yi{;#UxVQ^~91!ei}u|CjQ>a$z7d9Ilv#& z?WYq%YPnS$Ilv0D;^imLfhD%vVabe>dgGpoBJP7?pBL)eQfv<4 z1(g+sA|(f?_H$dl=vqQ2Zg8=+5(Hs>l!vb~Gtzfc`#JignI~eSgFKoanL}6;ygCE# zr%#H5Urh=36=7?lqmH^KDSEa6?fV6tnj!&Ba3@W%i16CX5)AP{J6U1TAAh;M@tDV) zxb(d@SOwfRuo87E3!Js2-RGpdwHUPzP%vtS9^cr>S1hmzsq}fV607^QO5RnS`F`ID zww02513;o7Lz-ve_y<`b?Qm%{GJo)B1vpiyoF!C*NRJ;lIX%LA^u@g=LvK`}&AvXv zrnOGR5g{&ycOD=U^!NtEqDQSUTnF7`x*>N`Nc*8e_naW^?u1dt`Z`aW71r`N8D`Vk zLBA-*w^S(wEn#PTHGSR(Yrel z4P+tpulYKNB6(YNI`y?_e7+U_uJV@5RnnqrfJnp9`4uT%zK#}l7DUw8>~8g!ysC83 z>O0EK;Z+fri|z*3-Z#I*h%2vH+uJFMi`2FDnCBWsy#aAgkb)NotRV{l3v2nx0+FXF zG<+w$vqHMHLVpXp9D)r35^d1`Egdy75V$Lto+C6kdnd9x>pEBg@SS2B)@tLL+=L$ zwQo_Edbg0y`U&jxL(-bIh`DA2>;TQ`BIm~F3$!*qQ+^I=U31QejDEhb&7 zf!Z_9Ing6y{M_vx!A35{R$(#Nbpc$WpA7^#yC4#Bu=v??B)Qo|Ec1srO%=#tr7UL^ zd9w23W$nlNfD}cEvQ-tfa6E4JKl8;T+jo;loV?d;hubq2156L8kmjudqBq@8(Vm#a z2n4VXVk(|F)1S&y4xbB;hL4fasQ4pj}bjaIqAkO+#cp31D?`cR# z8yM3~Xz8>fWm?NnW9wZTbf18wN>E}bt=dRIThvjOc&T4O&eRWMRYjv``p;_eEt7=R zZAOYtSKoDQkqB6^*8IHY&p}*HtTSA#ej2)N2wF$D8bAUe+G;pgE*;6s1n|BJM z^wCayt^vJwLEK$7)=wzq!+_3*k&WPsxPK`@84 z+oeBZh;62cw7wEdD69Q=#7TUYekNjfkOXW3Jfv`UVu;sh%&-Y52>zcXX>}d;@v>}v zs2(>l!HKsYumuZ=6EVOJ4G6*4C8rW|Kun!C!B4bX6qF_iLLW+6gq^)h`_BzcuTr} z-h_aW3d(hB@hge})#YljzA-)?asLI+4rm5aGfr7F_uMmv=od@S89p$7v4j*{kiTn4 zZ|kF4ULZ!9h(?y|SMf+iB9bwUE)1&AC2VI`B z0esOB3ttgEB&kcAd4df~`LUA2Sa|arT6emz%A}=}nQ9N0s4*bfoK;i{g*W7d*6I^M z!N;JavuZ@s624AqCj~5@e|{;0t($#MiV;Gz!M}OR)g}y%t`m2CEwe^R#5+2DUJML4 z__Q2|LN5S?i)S&^-fT)YNy2WEs!v%zuhk!eiK16YChwgNHGMAnaI+@z&!vMWA&|TE zaVsq#xv#j(#tcZ>dK@%+-6!WApd9(iT^B|pqU0S)v)=2Y78Pt(xn0Bkeo(D6+@KO2*-lIK zX0WeQIM}mdRfsT%Nc6Y9o`r`++9Wfy+TqXJDWJ{@Wtc!a;Is%hEcKeaMB1WCXs|Ry zh&d#OuV{!h+k~%^_gp4?S1n`u90PWJwK<>1;U(8lHI$Vt{l2OxV{xgEW%?mbYvsd= zYFiq8yh>j|DCHx<1Yc61xecpr%YoNxS~LuWzL@LPnW)v;Bv3(?glpY`X07T>fqPx( z8;;{+7&)`kfrDK9D~$V*$kK@rbWsL-@f&T2e*xnLpx(C7P(t=CAMAQ<(%6v zX74!@dWNWEEGz$8f(<;AxhG#E3t7|15VBAPqh6gPf4J^k(O_@uV8FmPATb^}2`!4( zq&laO(dq3V=3|M^49>S8m0!r!A))VmzO5$DJzKlvmtoO@Rkg*83MD_jh5~L(iEmaF zbr({!%q96}S>fCC;v;-%u%SJftxa3@r>Rm4GF4|JQr8KmmxdRck5~&F-@cb!GA(fY z3Bo!nxxv@D$*N2L3X%$5Gfg9N@h1LetYTPhf3;^I{~Kxa1UIhfdNA>{^0%kdNQ2ay zBHZ{&^?=qt|DEg_A*&lF_uq^RGHec_WTe}9V)zjvQD=e1uW>t;ZW%8&@HhHjg`dk9 zr6nifj3uwCA%zY(>#6v=P3fpCXaSC)FUO+LT|b})Ueu&msc_Mof;@bqh@5TR+g=n0 zk&+;=_!mw5u_KY&t$Garn>WA}pd`=}%!i>6A*aQ^)*fAO&vrtRCLh@w~m&5GaSJ11*MZV|Et5J-kg0F@c z1(|MBPqtm_$P>_k4SR&}E%tGvpI%{%`L?(!`C7F>5_1R=^8Q6hU>G$j9~yCTn^SIC zQ7TeW2-UP-%%DZp+qOSoE;=wjVWsVtK8K1ng=kKQ|JKJjL{|?%S=Fpk4bsH=A`3e=yqM`|a8s7(wmEVMGVI+&{UXXy z_mt?I8;|sMO6j_p_DXwxVo|gU2B&apC>86=n&y=law{S99x<-usrn`EOFj|SH@Uj+ zZdlxmSos}A^)!hc>l|IdkG20sn7el^k}SzGl7TNu`TjTg4U&2K7Y@xQ_)N=@AKg2E z^zMx*2{om{;x%#cUn9(W6xT@RH{{d6A5ckS>}DY7R#PZQ=ll3I$D`p!!&!$W+ar*z zQS_^r5czZ>ivOf!M{P~z2>VZQhssPQCd*&Y(prmZj|)G#&}HiXfZd#Hv^NytuUdI@ zgMAzWY%2M;wT_>PkmeIGk|k!D=mou z5;YKBk2Jre?--}|yYO_^xZROKgXaQl37x2B{cZwkS(s{v>hkbAhk`^2ts83v%l6P@nVY4K|e;@EwP`AWM%c@uS9SzYY36s_7WWs z(vv>aMOKWNtgo`0F3d&bwATTmP@)h~*AvV$DydJoIXUjXWH9Twb*siz%K(Ne#k{j< z9cP1K>_r)z&p9->$Ey=Mn6S}*Byby1FNNh6+Hpby?*tSNK;%+I7Hx&yAv8%xQR z=wZtNmi;u*+R9_k!Y3qeN5k&4BI;-0;(ou&V%{;zk(L)eF4pRQ50V{rXd*As1UEe6 z#HeOKr3}xOK%*uIgChJ`j|y{D=fhJWub7lwew_YBXq)ewiS3)3m_e~h&@9A%yE!ps zo4s_f;XgIS72B;O%jZYXD-le7V@y$lSy7TDzO%(K#Z1I6PdOe(2KpL?)?}B3UDJ76 zbr%f8J-Karu!>yBL!P6Qkkj_R%@1iu8^n>1k4mUvs95959pL>vqn7uTs1b~dfW7Lr z_}95puaRVO?K1mV0B>J%mD~mfbBM)LE#x|Mwj;oQupUiw>v(aDw^@;PZi>ohDxIpP zC$YDhXFs*z!D5Nn0t}45#V*95RgO4sjHB4o;@IqQ3nyyibXu#`Z)#}}ZP;ZVnR$}o zp;ESe@S#V*K3+7iAwaH90t z|8&1?)UxL>q#U%J`xk%TO&taj4dW@=|AeZzkMYg$eMf(F`BE=dqY)pnCRK=V?p&No zs#c|$I#R%A*gqYuV>YHnDMLTJEgLf{mIdSw=}_RD1KWDv1d8vddVNX|n!;^5)>We7 zc`7{qwuC;r&}a}UgydQ1^Lix8R!GxSxlvktX%u^ishY&;NMrp;#WI@@cpVn|)U?&4 z>VB2XAOa{j$#5P82d7?q8@hOTm`+5ZRU%@Fp4%)APqZW*;2m}0YF72NEHu>c==Bz< z$((3khHQqkq3?O*GY5}-pY~YavJHTwVW=3(201!`q{b~o&@mpH$+^adxPqsg7L8C; zGZyu(#jul8wN9TTgaX!^j5d`N5f1I|g|`M~tt}s=!6<<==h$t8x!Zu?Zedq$`eG|H zmDv);@yt`1Ek`2+^0U2!*^4i1RLh&&}RzIZ-3zsOPw0@lw4z{XfIQ_ytR?UzAJ{%h8;2`Yy$O_ z>FM>i;%=uQbjZStwWplI5cX?MhtMz0HObI^-EJ9u{-Oumzp5wyEzuKJK?~3JE-9%z zj1gU$?9Yu5`u&aAT~jgCq^*HAFy-U;47X6&d4}>~M@PR6L$>i(ho*Vpo>8F6(n})3 z6anq2#9%G+K+0Hd+5Kj;dmLDf>2BpVk!eo@jcRq}#d&UrCLx+u-~kGb1_i2e=_?#7 z%N+3NdRydZq4nv6i?IjbhzSL$BO9_L24iAjM~etBypuc-lW=gvEicS;F~hQ*%rpOE zJ}Qj+ofm=d9;eGv=7Ap-uU0ISi6KsR)`{ZN0d4l3$QyYx%{bW$52mkW3)m{VO7&O? zZ&{RSv|eb7=B9{T92VZ~=@l?z+6P8G;+V@@3~$$_<}XQ=fqRPq+oBX6P*L+2Y)%Tk)y&q^t_;I3b%{k_xhc|!@ z4e#)Snb@go=rR$&a{lCIK#%!3YZEng zRdj?dO74+j9_GtVKVU|fWz|V3nih7aG>GW$VqCjtR0Z==k#KH|dCuqmeQOz2b6GiN z)O1%DUmF8hOS3omZ~F-~8#p-j@X6(6c6MK?MqUN}Qo$-}+K3$-vKG{~g5vbGOKIpz zRn*Q4$6fgkMH>w*E<8IC_wjY+jn(qVj&X&jf&E`{rd3D1_>oZTmZg`xlE8O8`1yn` z9)L8FeezpzfQ>ueYZO)F{s@$ zZpoP1%1@xS;H4uVADnkkO=<>!j+H6y@IDt+p`>Pm<%sMVIaf;T`hq+bI51ZBx@7}u ztl+%Ll5RXTkQiHg^u^t@p2ZWPLg&N2Q-1ViLyVtM=nzFz^F(*^!p)H#e5UKv{{~!W zA+3{cJls3UKji*cbEMf_cU&6H%qW3vl?2?#|9rxv~Iuo&^? zz%ybw;w}wqHe;T=TunFLc^aq8n2YRPZvN;Q_Ot%Hz9hvE!$p-npVE+2%JRq=V)vvI zoR?U|He#RaOKt%9OUSlf2MjcXv!AfVrSAuF#6vEa5ZXT-*1;w$_6J356o&Y5sY#KE zsWl9sQ4Rq1*@r|@CooTn^^;E&*YGTNo?_aKpS1j&S=h*m|7*3cqGcm9BmP@%>y~us zy2IITA@_&38_pI_yRZ0`^En`6mG{AIg_-?<{}VMB_i?h5n1BEgE3UAM(J(hDdQg5b zq8}94KR9>4A^8Lw$do;~&tOU#HidEE>dK8Gq5qzdII>2c(jjhhw@HA0Fl$&a)?uCZ zHvgl;USN(;2CYv9E=6qNqFa83X@1w#&?@aW{BYZQ`Z{;xd zj1IC_@?is0*>Yh(cl<+(=f6QO0JszHPhel?tlTH1;*qZl72_B2xc$la18ACQr8f7y z58xqU=A#v^Hximjgg3C=CSZ(>e#79_AP57`%5FAXlgJ&{DzLr}bc;!&uP~_{K+@z# z#ktXNYcBU2!1wVDI^NS@xG!h2@y_jH770vM!5w4%Mc{pTAO8hZv25|+ZV(NvBT$M) zH5XmjtBeY1e3!TY93($!GGdlu*Oo^3V?a}XQ!2SBwj05qMIUezfhf)ha~kEALW%QD6j+Tr6My6sX1&%JmI@*fP&I>ZYb~jI&&3pi z%g|zkH^#h|K?veZ=ANI4=z|6&0~mwmMdwC6Rt_8;yx>8~aS0p%VplABKIpqm5wdV1 zFCL0g8bpRBg*f^9&`%sOg96;IVF(EMuKDfh*sMgovGhmg)mw0$gzE8L7G@W~8g3W# zsv+etOEup0k)3*wnoUoY3<>H%3ABOuwtoW_=v>`zzW6(GE+slH{|D3Y1s^D-NgO*D zd2k|;XBp{1NYiopX=&KD=vF1d75JkoL;5L309RGVoOy+2mVW<1({feiye#xau%S@0 znkPzuIecWLIBaU4YkFN8L7!|)22ZMT9q|{TCpfZh`nu4?cj&T06F+>?w&?NtMOuk} z!tsKY-xzrK)FvxZPDY$w=r^QuQnR#pUiu3}sN8%&QDZ z+~jA3uSMzgWn?#`uLj1ylN=Tv>8l}E#JCKS3`hri89v+EU`!c8#R?O)dFl`jIZ0zi zL9!DlC~Tr*!BY~9*kfU{!;6WL=#+qku?Ee~L@c;PQKJFM<`jl7WS-st1J(j&vqW8# zhaOk7i?>B74J7myxARZMc#8!kL(O!oZeRStsn9|wlaQ4%ZzWY8@H?0AoaOio$B0OR zB)6jsBspJ_4}W$ha68F&OxV8si!s0xW<1d;|M5KW&o{@0M+M9d)=G0YT$lPHq3FEK zftH_?frlDth3TAbDNG`LPjfpbNTx=7w1T%`#;BTdj%fCjQCWrAwQ;k_D2Jv*&3WQa zm9H}rCo-2UN6)l~<69$AQrZ^bYtiO1oxc2s#1e3V$QE{bFLmbNU5L~p;BNo!oPyrP z&1;294}x#WXvFg}9HafU*H>6-yW&jYaaXmlk3x*iE`gZ6%$nLLxSEg&A7D+&1+tq? z#EBNM8>h6u6({<67rJ#p)`G^4b*ypJJvMVL*x+WDXmknOprdZRgtH+T!xS zADjf4X(x3w19T6>>qXxkMA6x?J+Yrz#Yf*T&3st*hLOSokJ6?DM_Sl!iy`btge_>D zl)&6Y4cRcu#M-|(uZeC#|35Pfa?|({9iuW{k}Yhoo+(r{MDQKuR&P(I1$An{U4Wui z>%zx1$wSM>3=RuS@di1+Cv(vuWU8hlDEWCc7kkQlVa9{SnqT2#Av(75*1xu(^v^rR+nTkCQ{ypfowe zU}BZ=_81Z4XY^e)(fS%fKkW7{pg3Qj~yr=DdJ7cfdL2{1R9TbL#ySxqUCcLWduv`3&Y6X0k@_CRmVeN?ANj zWbAD7shl{-Al(CJqebyE?m`D2i-S9tSA;1bm8t!6{%kD=wH?Yc>SX-e$#rYJ+O&x? zCh}&bL*^tqJ0;8rzk_F@ouT}kf@|lJ9_Jk74ZCQEUnZFO=tQppbNqP4?SBs0*gTQ6 zde<5LIm#GAu!nX(*k{ug?6NGvw3dE|3me1Ytpy{FcZmaq|0rb+BZ64l^I>h+0kh{9 ztF-GH`gMkkKNtI%x_X`ApT%$n@5mXNY^_b!t4_$bU#-cSxwB1iZf$qu@h#+>THPr0 z1!Hb_Fiv{bFWcstn#CNNKIyFTHQJ#ss>??i9*M;bl}Al?A5nJ9|ARR{z>Gsn%tKe0 zhgj#BV@SnfV2mSt58e6NQ%uDjAy+wUaZwW<_NpSg6mv8SXb)s zWY4)!9*TWX_1sio1nP)+i?->u{JJRf9Ee z_E)8GtY9=?3r1IoWkDoGAk>>?kQd$M2*cxZF*P1Y{t6@Y~ zeZzLGo=BH|8fc;u?jT#{^MYs6=J8H^Q!*#^chFsv!j6Cm22Wvq(0@MvK$SPD`y$2f z%#?DkMQ$=p2y!m|-vhl(0tSE@+7aar+G-7dIMnEul!KE$Q!gMFNqA?fJ(K%y7q(@J zJFH8-=+#Vx+;FXN5&}rXZttKd=}3XybD_VKnf{|id-jS zj-S4Fg(c~x8mdtxO75`XTgtmlC${xBR*uL28+=I516{x5{s$w1`>a}D*O z0UJq-2(Hm41*%ggUG2>nd@v=}b5Gk7;jRuJ7 z#w@K|pSTW=C93$>Kx^lJU38&Wc^L?Pk`T9`@~f8B!VZqYGremYVrjx7uS~#sC;DK< ztnCV}`sNm(+KW{ch1+8}^I;XWm-QD~FlRYM&m)1TF+3k%c@*|JfosjP1e5-%yaQ++(CVK9P82)rGl8{BiKn$|E7s@?DYAjAB(y$iL6+5&< z{I4XR_)rom;D4dq;FsyVgq3>zNL9^AS?q^fP}e@8l5Ar0T5%^n2M14#7)PQ(ryoUG zu~9P+TSiQx|9G^Lh3`|0;1>Tz2_AXO91u`65Crmk_FIl7N3dgBGI2=j4dTUcr9^OpJh#LRlXP9iZ5;V4U6>Gu z7Sn?jD)uGTnbZA&PRV?>GF&OyIf#L&PzX$O)r1IX``|FBB2Zy5OZ3swbAS!fPdkJE z3tqwEA%C}JK6`dk85^lMds9EApp)nuco9mq9!x|FP6E`h>-ie9`fef0qMn_7xt;uP zJY_9dbn-|`Pb>}ROb3-2u^5h}qB=W-2S#O`E{+3gB%2kqRal>E1sbyA{XkuxE0U&@67dDAxs6|9GSO(;R8C{H%1qLd zz4m?R$K>A7u+^?yZ;y()>0g*qXi;k5F;G~8ctm#pjx;T-u!MKC$>3$q{MaaaB<+=8 z`uz~J3mBF_TSO(GDR<_Qi>1UmJ39@pwKS$fRGgNs@#iG=yy=$|A`iD{yLWc>hk0Oa zn+Wcs@=<`I@@WcFu=%3B@}JQAejtq`$tWJ`mHZu%oRM7IRs!?h1$rH8d^8dsF=gj8 zmsQ8FJ1tQihq#_ra_8G?={-mc`!`Zj2dEA~oEcCP3f-oq#wh;oIrsUCJF{fQ7~5?_ zxWg=Tq;@!*3(3>lrs&c3NSwO9(z3gU8afmC6_<8+ni~(v3E9Jz*LWiH7)J)|4D*9* z!$dKQs28$q9nz%BSqTp_fJynw|G-a=IXpM;X=H|vwy3kij{n_ou!h#2mCZnBG2&@# zRfhsI%P197`Irme78$NU6CQj;X6YOLD(JFFsl}+a%WH*RtS@5lb&m;k zdcFAM#e&6LbB;0YUk$Pb9lNNbo;y%rLSi}PYzR3A?gRyUv9{*&;82~2z$Um|CCE96 zT7B?`1pkxiNMuVDb>I=%y+{q)$y_Gp(hybgTiTDl0DY4q%MkscPf>XUf;yX>v!?(E zqvU3_^;+50MliD?=Sm1j2Pof8&2E39^wpIdAf(B)`E3ki0My;Ke&Bi0=v|V>&pK^q zF(Z`4FP}z5X0ZmOF~$B0?4H!XW0Ko&RTtPTgLD}YvsxIu>P(RJWjwF{==={aa-RAz zhcKtSFnSD3oj{RnXn`%h(vVP{5%s2`N1NTSY75+1oYQKQ=afkuMEz)2t2u&lK>JGM zE7{T~ZgFY>#ys(Fy&b`?hoTQ@QDSR%D%%6x631^OOj-llzGExAoA9>y_OmfQJffCz zoUPF9{Db)_GZ(a97y>}tGg%=z3hi_V?`7B*Ya3O9{15*;*%;xN4is&sB=3dGj!jkJVl7>y=Xd*L_ax&TA?>E6drrF^Agup`jFO+AfL=X+# z^Ms3BT(muQTA5b(Jau~MJDP)enU|=Jh4^B?529rog9KTV3$GImZAxT=Vf0i!TMR-_ z90p#v&NrCH1LP=km-u+boBr0~w78jpl=qagRE-X4!}6^QJMBYpR^iiBhxZaP z+ncED8aSrZ*&*4f)u5A=`T#@qgk3{Vw7HBQY{r{bfX--wo!twu!j@FK5rnNUw7;e@ zRn$gr8m@y9xmPp$IFt!4EH@JKQ!M;|)}Ic)_L(ln2dR;lC`kohj-;BNvOu`iXYu+itI=?zH+aiIAtfNjR=j z%FmMSRmPOV`Rbd}j{sa|YX5q-2`4MkL+$0v{L@TKaA7(g&4tZYlors1=n zKs0PScST>Bso21FVZA|A(J?Y|sS2;1u?jIyk@$xN)0sP$Dz?9=h=S&~+Pn<=BTzkpS z;65C-mO6lXc>pwBB6i7^(~jhwjAEz8%#ov#f@MRj+cZu-IX9E z4VzlCU8nq{ofm8yuHX*s9IHdDE2U~v2_M~9#m|cp74?+a^&?7IO)D081q}UcfrPnU zW{KqjN%@ZLpJJ*L3JmN!ZKTT)NIo-x1+^8JEq$8)T+$;mX27sJD54*RuGL6k`;B5; zG#Rz@p+Kd;bzH-b>m(VJkgg}|G^~&kAAf-cIQXy+!8tV16Ke@c^%Dheu=8IsNd>j%BE6k=62cf>|r{U&$cx80Rnqo z7P@Iprd3-R)*JOIS3-U=O&>K}=2EFlHH@Qq7=Fs{nnq$moTpD6Pw6RCJSS#ViYBZ$ z=YUFU@ShRQ>S+GYUHSvc^7H{So~R=OH6u17Ds03G5mNeZKdf6Ef**!ljy1y6&8)rM zUuZS|;dl@ZBbN34a6I;oT6h*RY%a=JYQJ#yR0^o>UNNZ`wJFr_ChBv!B;carNs`jx z7j`h~sghmiMg)C8zcq)8MkBq+YQ!xxy*XLa!`|*FbW|1ZJ9_FN&KyA4zsgFj#xte{ zciCs|^eI|9M@?I6a!ZEu(kx&HepdhnuiT;kF?hYjInh&cUqg#R13Jgu2mnJ&G>GHl zU3ewiaHWddH+|eM4TQ>F?1x#UQ>j}Sb8}572-x`CEZf7$@~&5?zR-pQDMk#Se23?Y zwNhQr0@5;Y6$v{~w^4}JlLL?Nmc^}Qkxt^51(i?*`KvKZWIHvFCj^~odULax@e4bd zmBt-`$p@(@$1t1>N4&MeIGKnB^EAGeQ52OXyw-kN@rgkFbkK_L6nuqTOsk0)Y{n{& zs&ss6Og4jlA%-`N_DUf2t+w!G=t~{R>PN(dY(ztE6Dp0LMwlZkl_2!rkuaL?BdX_igN2ncN29u26 z_09AKbh5nVY(fFi90s+0YsLf+n#;O61A<+#QgIeHr5k2h04>TD+1HkJhVf;h#A)Xy z@SRduJ9f$Uj%9%{>(!;{u9Dx@`sPL7^6uNA3pvzKvPxcfYbvL5%sqW><6^oarN&e>}ty$ ztR)B>!#gt=s}(cd$KRHB=if6a3|XQkGNrSU6?=Rx4t^cK(}&qmclKLyr3T5OiV}PG z=N^>TDM~QZs)j_xhFeo~Wb9AON*sKRv_-)ZfD@^!(;C>G2+;!+eOq|xCd-!inB zg4_^2j4&P0-c5_$1qR*+gp633O`#KWklU

ym$lygBT9p46EU1v?-H)z1WxJw&aS zngpI&#$SxS>~xL=uxT<@0^@BN#cZ$yDeVSPu50%g$2lwFmh&n5t7~OZTBb3`=Tr&Q zAN{JHA1k|DH%qZRLux(aEi8ot-fa-EpTjO3y+*k$2VQT3lvN_WiwY%&hU7*#I7xw_ z$nCqxnd*1x_&++9ki^&epVn)}B{sAo_!FSN`kS#OF*dv6)#?L2IQG^`5TC?_6!mSI z?vXYn!`v&U7V#&CXh;m3uPAzs*1JJrrssQHY|aQ)@ehtN0N6t$$d;^$u$%bU;Ojm= zcMM3S$Gd!i56k;SBse3;DzRcQmTv3AuBjeMlj7N)c4}eBJYEY6S10yBe=Ko%bU&_V z4bUSF1sOx^h)cDFQ6acN-g25js%2vyP&a?`@Kqz5XNe>Y)uwz(Pmt3mP1n|psXhOBcYHE@z>Tbk< zrmw>!x7j@J6b$1&9Q05bINAn#UXMDeVV16^T@Npmp`3Z1PIzzmZILmzSwG;eB;=F> zryviopz_JhzxPLJ`<>wS!PCD9;-ePV(9=l5&bCfRFk?d6FS%ykzn<^t5bGuZye-|3 z7Hl!F)$#{Lu-p)KmL@f4+P5mL6gjPV3f;|5R$wJb0~GmNzM+HKbqx!0F;M{hVMP1w zh}0rSwy}0>%s6alSsg2CZ-4B-oK|TsM*(ng_vXNfP_JHTs2^uQ z0xX*LlQA6Id&s6cW$=ZsHeMf39*XT*@U31$j>5>C+|L^FO+zI&o7NaVw|xl#bH^8= z4Ku~vUaM@mtlPL$``FYLY%#(TIv0%W^~X{uQ3#ks#jaweIruH;Y6!bNjjS`Lv%ffU znDSqW;r$MDT?4_n7UEXEN*Q8Y6P`hp9TsNl7peElBIXG9bs|~&ct~Cv=mxhI0NmK_ z96ZLB4uGH_@Rr^-^pYyKf+cEhm>(8G-E8sqi}!Wx=xz5 zSM~1C`sr2m!q%Pgpzy3xMa|Mi=0!C6k!WP9X7#{MdqmcAXl5`9R`y*K@EMfg$Cx0d zLF`ABGi*W}F)QTpMYYgg{VZv#au)5KPMWqFWQqx#*(4ms1%@{PbGu$l`Sp^|Bk&du zDI3PljZ(%SGpum79;#wX+aRX@8Z6AI#|^$JH)9~t*VaNN+aIf=Vwz*f=6`u^XE1pH zvt4E1BJ1fwq26*8R;QKk>JS6bOWr{gws)=_s{vi1^pylxV?m##{Iye18cVem;AO{t z6XbM8w27H@ZYgE$w#pP%X$w8PIWC)_a|^B>gibVq^WGBMk@ySt<7J+0Yr)7}(#atG;(P zeA}oL$>esvC|$#WYmg*ylX0(M-}&MpJaSVX=2lxz&54c@&-LQQQF={6nt0JSLMrXN z6r5P!LB-R|Q4p*}K1l_{Lj}1B`h~C!pV?)|2J@ zR5n{@S|-Bo7`HAGrEe81=VrA zYr(Bm(%TzKXyIS$-J}S9f6_Jl048Qm9XFZsUYC@?qY+U3qK4H}q6;T#SopvUzmFfM z=W6=Y$<#x=lF)oCS=RIAo3C8=YmjE{z~I$OVxDkVl&&h;%xLpkc$ys!4MN0j(a%&N zy{=KnjRr#n7hj2p&c>~Mde#iPxlDm~Ujs zpu_eWO1Vx3Tk>Nw!VWX1x4|@FX+5ufrI8uyaA%26jFcs1SK6Jr==RS{aeY_=Rpjc& z^cKBHQJ*+5U3s0$tQvWQUiy!&)`V)DeM-t#E$}iYAip@Jt{t{Kuo#zEDW| zbLnfnmInS7gA$C$JKytwLkeJ`*rIW(pwZi_qA_i-Vf0VDY6bZ5!h$@$t~&Eyu9Srg7_K@ zQWs;nJH7sPB8oQ+qDe#4W^5Ao!s?qaVE9m%OcuZ2d(MCjEj7k=y^tRp(rHFmnepMC zo}kW=T=c}#VTkt5Rtg}>JL8o=yO*Thluw6=w*X}jc!nUBQ>~dF#uZ#QxK#QDZK!r{VY{|H6PFx7tDaKmOu;;x` zppNU_cY|+zEcV`w$FK>|AVSQbQ$ueTbZXeu>i;w(EO2p>*u3JnOsaWuFUKkQMFY~_ zzXWJOZ%9Wz6Jl2e$~$Y?tuQC5HtohP<6HUZp-fIGwox@H`ycY<%$x3wzsUvI9eny4 z7fhh>U&R7!&N=5VsjXt~yvT*m;L?kw!lri%JYSEP>L-m251*?xbR@>jZnd63__HfR z=8gcu$2ks=5&3fiilpKDqQld@@Dpnc!@y!@CBn>a=g5n4ZNQa2M z&6EOizs{x#P+V)ksVkc=|DsUEw|)yq2nUtSpnP!U_mt2;?2GWnif(-`Whgos20Olb^PF=~PHViMJf9v|)& z8*%oe72a=rZYD_VKshI*9n}q|JR&jMV9L4g52*S5Vp?-||0k$Y2ed8m<`+C}qjtDD z3AU^%J7qe#1it zO{q2fs_Fef!*VvY=GWqv{i34q*M_`N*UbU$ssRl~R7DIt>kz&f5#BNpe=hnxOoj)j z=$VzL7w`wD(Bqbt46T#xmX$iaWm^7|wXnX*h^&;50WxAM6irvnUipXXz(rO?<>=hb zxk!}3?+r%lThc_dsI_VZ-4a!Yg$1NdCOf8nsz19xDU?jg2DphHA&Se zbwH%u26cik@iWb7Peq6ai}J`-Nf;#zF#9FDgl?(h1;1JrC6?H zhiZp zm6Y1`q}Uu(hUtt{yQv0Db7{?~0Q`@S;($@cdQP=l`kSc5J2#m!z}V0SMHMio>t1`e z!EX#juojpVJK^$|ux(}75b=3i1eKfcy2h+}C*fHY& z)h$tUn-OzTVWR(srdWQ@+4v_wxv3Yx766F@8akt8Iw|HeGVNay&HjkSfy~;~DfHXp zOWZEo(!3s)Fk?xO6YXk(GmwA06mVR4U*tg&K_r7u*-d)&vBTdK>jdz8%iU%%B=~iF zN(C>+A{YmbUZMhFsaVdc?|u?Vs@JXhk+-+Qo;S2IE|(aG4ARrOmC@Kn6CA#YFd>dA zH(71fu30)U2?-E6Tr{bS?*l$BT_LETF*s6?n1q)wgX@nu*hTTI%+{NH?D$t8kdir`e*_h&r~Wi#qo#0An?Dqw0c;FKlS~sh ziG05il0IoGV7{WmTko5BdM!ODTyehQK}+p=j$ZD8up7xtKL*%%egTpOKsp}O7nc)# zs!bud(GRsY+;xQZCA_fb;1UfhqLnZ zFGNtv>~5v3Tnl7=1DLFFR~$9q+H-vda6{rRBtBQcpt;tW$T1@YP})~}$scND z4n=@q9=Ub(q2jkZhQ0|GO;%$&SDdL|){&2N#Ba$lPn%Q$;}wPzj)g-=@2WSt?A zS)fi?qbNKiryrDdL*ekqM!{ z{>N3_iz3(8VXEMn?l!W~-vpxFlD^0Vba>|gr#Y_Lc=XXVszc@1%g@OdC=Ioa(8TtZ z56}@(blOXcNdQI4RO2x3ajHqT-q2c!;rp{_i=Rd>W&fUc%&P$%>wcP{nnxc7fu}qU z-r|nC6$5d-lo}^gt7qn@vUf&-4RF$f;r<$cgg&f~=!u@3mbVTt$WG)`3@vT@gM@Vk z^JI*-=ROrm_}Lde?&O|!5vWjO{Akx;CJN?k*G`d6KVwz`5AwUYxDKMwd z@jdy9}=%!CnwG*osQK1UNe-vmqPQ=t|+Z47k@>S|)Kn{-zBTTRGe@6i? zp1Rly{w6MYBHjzM!uC z9wNi`kA$7X0V&=L#IHR_Gen$ND<=1XemZ2-&F=i+U;W^T%TXVxl2s(Y%(C&3Qba{u zkMpNH>5S46q;IR2OZsmU_%7Pu61Al9w+k5h*Ft4(AuTjePBSuk+r} z&W@Q80aoPt9Fj3H>$VqHN5UhD$5IyiGom|5gt)z9` z$K&|{?Xc+NX>sQBC5=oTLm|#(AIsd6j^`F-Au&&$HQQT8HkyNb-1PRgbN1RCTN`N+ z|3@n!QTI{!Ezhm;^iT2MJ^kN{e{(cTW5zz9HJ1;3` zYig23*o@Ub8uHf+51jY?fX~geg>qOUbLUR#Kcydu>M!|<(<`5v1bjo11qf<8zrTc@ zAvkxS00W^p_oggrmTDY<&aWbBO1KNPJ@ateJzS16elY5kR{&vJgFk>xqO80LN0KIO zhhxb8lwR)ouflH%Sg`z;B&BW0pY%L{#06~kj77d8=8+0@(2Iwe+pT@8N)r|`f~WI>hMh?oQ5n|CydBq zzjj{o*ULAc%d~e5P`av_YaRQ_|)JsC4xv6t5ljgrKc+f%S|bWONU-tEIFkaHJ8Z z5Wub^H1aK1ZfZ)yk9JqWx0c52Ws%xC7g}HJN?*fG0RE#T)?7w@?7S0xLDl$Gk75O@ zKn7O9y9M&`&RbN|_SymT^d$i!5h4!(&Zg5rNm+MlHnT7J7LX1RKP99D$E{K5Z`IgT z1!RBaTS_-GLGoOU+$t}Hx{*cfNPv^HkWw@|J#mKEhWGIU1&}IE>%?HDnoUwI7!02R z5+{E6T6$9;l|ZSF@%jKvRgqZQfcyA>|S6DZ-;f{?q1v| zUEDU9UMU0J1&{GTOG-(#oP2!#g$_SLk^CE3EkYgnb2=?WW)W>~ppZebXW|d{PX`m}qB^;kJfn2A(1-xRdrCFfnt z=TmAH^`alA@ z&X=lBIu}Gj6+3RwxbcR!M0i$?CIIo+4;=zN@+%C|r>1>(J}e_2!GF@^$gBiC%m{KA z7>5NEru3*&?4(Q2GiMtTX}gUtaODV9lpRsbDss+gX=U^`XCqKG(snct1^b_8P!`sr zepbXuj-pum#WBh*?yLU-34KFdjxW2nf3g)9-;_vuV#TMtXT}*+W_toKeRUV%_Czv| z%p#pJ#$5&OjVYm*gAzw6p`V)djjYF(yAo#D#{zlc?3x!y%!XfKNu7ua?bv@>0>lbN zk1wFDtu;dq$oMr@2Qq$}T|;yFGTfNLQ^5u7^G*d)-uyh!&K3or4#f4*9}SPSK?1Jh zYEQVy={7{*2StG1^N2h`>+m=0ZyJatig+kQPCpC@%3jdV-dCrFQ4)Xnis-Ht+ENwt zybpB;VS(IfRy!Ax(V|coMua`{QcvIhGd{%?5Fy3aFis%bLG#XTY3#@iqFK}^lalp1 zC@FL^G759)U{)f@PYfLdy`<(q%ELDDxdPzw{=R4c^-zJ({(7iv3B~{q75GfS6r8tc ziot2w8mMl`RS0;zS31HY7`}PJU5dethSCxP8LEv|+mNlXHcP3WEj7tCuJfz8TO^Ti0O`&$5sAR#-E8F*a~o-egg|`W8~5HCEkTubzGj zRRecGPKQZey@^QCn4tZ_I|r!E?#w$4h0TQqGzNh}Z>Zy|M_WW*Q0T3(eo1W5I592N z!jkW=x@of{Aro+k!}#_|9HmFm1Kri_2I`0%aqapqZqChLiNC*6x~!K2>J2|=3vM`! zcXIvnU0hwpVOaOs=>~NiYG{A}3y{mg;EP3diyd9_Sye7ls5U(6Ok}_L+ok@uBaJaG znU{ZG)9}*kL3y`sJ9g+t<7LE_6fo$Km8yG8OqdDw)eMwx@u|gMFtYpG${s^{{Z!y- z{h25;QY-F=Q)?9tWpj9-=Lvs9wxpohAbII$IM&I*;kK`yyaRFwsp>$Xdp_Ug2Gh;K zo*8?-)qroBKC-S5Pcfsq;z9B*sBwk`Pssuf3;H8~2w9n&x-2PfSri9RiCaqcZ#jSM zOQ+j|&jUS8Q}ooP{ZNb4w4?=Fde5qzZ4<5zf(rb0iwQ zeD>GCr9^dxVvDC8N}JoTL-ve>d(ox@bJFm@avVMrt7I&{op8+!7kYsj3R#6Hj>Ez3 zy7=yVvgyf*9Q%fTze^_|d?{_PB1y^9uIn~`o|IuA{$r`i3~zlOFaN+e9CgzSU2gXS zlg=2lwFo5xF1k{|WLIHk5{!#!k6;(2?>;R+gp1n7+g4T#u+;?+;Ii}0Hy4`V@~E2R zQuFNUuX#AX)huF0a&DgOKi=Wr?;gs2XT#Wj6AgU-WI@`8h^Gk8)~RUSI{V?{jJbaQ zj-o)7FwHe<(@#1TTq`r^Z+{Jaq-50g#+H@84wvel-~9!vB!kekXix1`Z9N-~>9j?l z3Ru|g{~^SPip5%LNU`+J#m>#8Z*A1Z66s#O`1a{!PVzuU#^=Y9D^VcFirQT=g{oik z#6vyHC|Ls@+I(IqrdWkM+Prxy2P>{Zeg~cT4W(U!!ukc{SA`S@=!NHC0-z{q0%R@p zslA^bDY9Vza6g!P;yFV1KhjJ>%Db}bmlG6`k;BL*c1@qhMgww;X3y0cw#8ZM%hTdf z>T}vjpzN0^Dt~r2ik7yfgO_KqP+Cy+tu+xX>cD`1!;rh>od=Y4#az&zLp>4j{88)a zuennwL0l|{FP}4nJ=QZ<(3rw&{a4XtT3#!sfWy+kasT!`SSa$e>G&?7gi(xU>V0l| zZn^R6%4#5-gfCQd`(CHIBu=X$=S+pvAK07|82vIFEJeeK zjjsjRh*q++&wW*MxDPTT{3LyjjPPhTCOnlTO;R->K_^`wA3ETU5CV!Ee}8;{d^`h( z_upY>RuJ>~tr@p{zuopL?aIH-LgXeEN-7Ay-ThY~y`8xY(zT*&GJr0ds^6e*JvsS< z&zPiPu(`Y%%;W=Xsy|dpkWJtJwXsa;xLQy~%9|T!gLj&<1i^2`v_?6giC?-nj3Jfp z7=N8g`|oNN@(0edx#=Brj0*yXg4jV)f(JP0U$2V}RJrAjsr&TO5Mtr70V4z%_*LJEy!wPs$u;8x>pMcy9!|Ol|}nfcG&d>DCb8_J!G(08dYBQv%1>_g*V> zhb6g_n3aok!+xBlIq!b0yIB@xMb8?8$@>V^GPV$hNg7p92f~RqW5Hz$1xEPxe^Awz zCoJ*93*GtzCIHD-*}KIopF8t)$A^JJWvK>4!D!emH08jDNMuK{Bd>_VY&) zJf$1j##cv+ppLO7_F5vuir&N*&U96M)XeFtehj{8tIw-GLAR{cvpEi=bsV_6Fmj05 z$)PqF5QBWx#Kh&CzI}p->?jdsp*#ata{Ul}^*e_D`*K%MVOir6%%QgTM;PKU&h09` zaUr>}F=p*h+sqq|ky&i^#Qrc%8!6aeMyx{|v=*NBW5?NN;pGq<{d(Y?ev9Q!AJFq~ zHg*~ESwZEKoKF2oV;ep_@IKcjo*m4L3rGGA=d(2LXN;q}GIxCI50@0TK%DR{H>zgjNL46zQ-Gyq~nPHNK)b9qfDfM)@pI7rC_Z*CLZV+d1BB*fCo6fU1r`!0 z^4a9c9L&Ax?Odug6d3-d=!gb{$DA@S=lg;~ca=SquR5le-_|KTObLJJ6MxWsSOIAE zilBKgigiJN-TnfcVp|h3$Y!?Jb2md7<*x|&|93aJ_G;-~jm5C=AU<&fq229Yv{^E zC7+4`AE;bS(c4zkfY3teAg^X4=e)bKs139?fBg9V3azx6SEL z3G$^_`ofus^kaGgSvJ7FVA>bU&7x{Fo= zZu%%UG)QZPPf>u#W-KMB(Z2A!P59w(@38ntEfeFy{zOdYK6$AUY`yFa-2LB@bM-UEKenmpSX`w>T5*z^U1*o@>E-9zLp=ke9l zUUKiViXV*ZW9!s}E*rh`cMZ?i8eVGjbYQKrqTJQBwvv1brZtQ5E`8eR_-@Bp5E<-u zC1M8JUcKt_551kF+BI1CNJvAuOp!qpF5pP2v3ISIavNO_V(pBb;w^L3UeG{!-l9j_ z!fP_CsDD-8cp-!j765_eg&bGFkL9UUmLK$4fu&jVaZ)!KHY#Vq2nW)50f`g-mtxw(o#NOzBUC1&5P4cbp!KBDN3iG%gSc z*NTWsDQA~OM6z2l-`db2I6QYRH$rL{j3hBw11sC>#}f$Q=I|dqhX5DYoJpIiMe^k}38h z>@&TFDT6MU(r}#&YsNz!}>%#>$2K`}zi68>_> z4U=zVA_z{$=y2iK4qIs`@O#ErF*Bc;9FS%oZF{iAkY6W@@I8&E%95@jJ&;GML@dF< zdH5>qx4x=*b;PYr&AC1$_MEc3o)gPpmq+pZ4S*etu3`0`@5OF1oHVUm$huMX@u14NGd(xi ztSGtj@Au|iNKtM^Kl&-%t>*g$ule`lEIixq#DO{=)|VGzam9C>e&zS0O5O?Nh3jxY zlJN-7kMlVJ%51NdH{|0_->u^?C41P2vf6TO6;g+N`(w;DD;>^&9ZtpH+p4vmS}~ zM@sx>+WBTnD5Bj8@1OUCzdc`cf{n*X?VP)U2q-hXki&+*&querK4TRS&r2mkbRKM%pt@N^R}+nq-8NQ%AI9>X@d1ZM?B}f zB=Yi#y5o39*EO2HSk0T5-X?prW6S+((LnL+-7hO#F}8%ME=<%VXEUe|LciKyewaO8 zktO4=fA*B?O>@lv6L7_;B|IaEA$oEmhmrOA*LmQKFq?&BEZQiO_-RZzj9vzik6tN5 zwE)Ju^$rVj74k*9<+*{Z>-hPgtd!`YtlGwoZ3vnSusd5cJF-!)1!LQ}E#(&@bolU< z}y4|3ErwhgigU!u)wU(F2Z_iP;5nG3SY1R)}|{LCLQ~mjtQz%jVSG zdE3}J8l;G>4H2*YGLjYJG0zLzGPhQA>lH!&a`ex?+pfl}2i$kk@{(YYAfg9PWH(o3 zv7ChV`7QiDYo$f_M!B?28BeCGO>`{>9~9P%u@wirzS!QloNJhEN1#6XI+(snY)B$n z>}+Ac9LqLNU{&Njp}YSRVGe>}mCf)O*0|7to5At4?VVYldrl(G>>|1lhxA1ko)V_u z`TQ0)y~1{T{a*50w%}2<=C4l0J|#W5NPOUS@OLh3Ip*HIzsc|V^MpltVxLZiYNzj& zKh=!ObRtp>p!Kd-Vtjem=ZgO4LxmO1zw>>L@q>WKboRlUh0KD0&JXR$S5a7EOqTKb zr!XHn#(_q`if3O~*jgL|j~CjsSOR9J=>`sdexrkyyWjXl($b{AJ^ht*KyX@EBd-(F zV8iSJGx)||A-n0Z?QeHKd}Te#G5FP@~kQ({0BQ^ZugUwGqYqlgp1sJMfL|!o#-(1RmOu+a(a@ zMDXY7946jka_(`oMP2%so-Z#!F>AoqC@+ayrw_`SLp_fW@q=izJ2gFovFuimAXA>> zoG<{-ZLn~KF?$tP?SMM$a!)Fsdk;(SZ$IXlL z1l1@9wJ_NG9mx{iNZ|@=h?(_B-sGX8AG9;%Hctwlso;&Oo7wP7ZfQaD&GS0MFuh>& zGV%GM)Np1dW_74cZ()th1d6#w#3(9#*-#3Wjy{;jq8zJaK0kRbgvLPl^s%7ylF2?wI8R zL)-bun7tPCw!x5L$$#Eec0D(eUhj)QYqHs!VNcvIrI&s43~SFrYDl|%*E5#QGG*Ng zURdW*npjWtH}5`yr60e>tU}j*{W`tPUxag6=tOx*7nF_k@EV?rpY;pkz$%UZtMHZf z*^h0~YjqXIq4%j#-#vS~XB|X;!ER08ujkgUbdk;qMvM{l$G?+>9RDV8WR~0}=FXmM znNspo5>0#bpAMkuj|uJf!rzpge*;O{0+As|&Uy@{T94nWihZby;%m8_*sRdH^^frO z)HQHh+KgXv=sQYkLLRIF%zBq5ggD3kv70=uV@S&VXWM>dd97Na7n&^vfMe1>4P>hW z@{L)@ARl6#?LK?&BA5iBMT5K4$B}n@d=yBM^Ja+KvZ7e@EwP43tJU}Yvy4os^L9_= z>%q6Ps!mtMdD|5m){-ZFkOkK^J!{5|FR;|j*p58H2&>R`NwqS-&4LzxgxECV&XlINejEQxLCGk;P>lt^MD%Jg0-oBl71*09@ey0$Aq4qm_+X%Ae0!8m0li#1LH;Dtl_|NFoL zZ3Osf^6BDf?4RZFLdgnGKc29C85lzzd;ISWf(dg8Nbi@Pem(X7S!n-fxBZ3G*LT0- zX2P+t#d`fuAKe`({M<6*R literal 0 HcmV?d00001 diff --git a/SS2026/Quantum Computing/6. Composite Systems/Composite Systems.md b/SS2026/Quantum Computing/6. Composite Systems/Composite Systems.md index 19f7a30..784752e 100644 --- a/SS2026/Quantum Computing/6. Composite Systems/Composite Systems.md +++ b/SS2026/Quantum Computing/6. Composite Systems/Composite Systems.md @@ -12,3 +12,19 @@ Example: ![[Pasted image 20260729215837.png]] +So to apply S to A and T to B we apply SxT to AB. + +If the distribution of a probabilistic system can be written as a composite A and B are independent +If we cannot they are depended on each other + +If the quantum state of a system AB can be written as a tensor product they are independent +If we cannot the quantum states depend on each other, we call this entangled~ + +![[Pasted image 20260729220918.png]] + + +## Measuring composite systems + +We can compose two separate measurements similarly to how we applied the tensor product. + +