量子信息计算与程序

1、1. H矩阵计算32. 系统准能计算133. 动力学方程194. 密度矩阵273量子信息三个quibit组成的系统的哈密顿量(i1,2,3)iHsingle1BZ?z2HcouplingjXy?X1Bi?Bx-x2?jx(2)Jxy,x?x期?z决?xjXv?Xxyxx由？z求：H矩阵H11H12H13H14H15H16H17H18H21H22H23H24H25H26H27H28H31H32H33H34H35H36H37H38H41H42H43H44H45H46H47H48H51H52H53H54H55H56H57H58H61H62H63H64H65H66H67H68H71H72H73H74H

2、75H76H77H78H81H82H83H84H85H86H87H88则有:定义:(5)即:i?y所以：(6)0,0,HHHHHH I IIHHHHHHHIIffX-JX2X3BN3WK3嬴巴I2|一二3BN-"2NBx31-H*sfT*(J”J”。)532i002IidI62Icn2III22IIIIIIIIIIc_x-y2Ic_x-y3C_X-y2JO迂4JC_2|BX-c_x-y3c_2I-BX22I-BX3c_B72Cx-y3巴巴巴B73JCX3y-BX-BBX-B73CX3y-巴巴BX3BX37IIIIIITT8765432一33333333IIIIIITTBz2Bx311

3、HITTI»765444444IITTIHHh方Xkc_忑FoITTBz2BN3I昱c_2|一H2|一五区y22qC_一忑N)BB,z3Z32r、f1c-2I一2I一BBX-XC_忑K3BBx3x3IIIIIIIII876口4324555555555BN2'V-B.Q222.%3,QIII III66ooI006IO)ITTIIIII-忑及尸一zQII1：IIIIIIII00O)UIKJ715IHHHHHHHoIIIIIIII000000600cn00300200-、00IIoo002I-2I-2I-yoo2I-y3y2eBBBBX3X2eX4cN-C-C-忑打迂火忑吧JJB

4、mBpBZ2Z2z3BN3-fi丸W林2IZ32IB甩1)61)000)，1)101),2)171)001，)1103)010),111).14)|)1011,5<iH11/1H12)H131/H141/H151H16)H17/1H18H21H22H23H24H25H26H27H28<H31H32H33H34H35H36H37H38<H41H42H43H44H45H46H47H48H51H52H53H54H55H56H57H58<H60H61H62H63H64H65H66H67<H71H72H73H74H75H76H77H78H81H82H83H84H85H86H

5、87H88#Iro00oCX-y2c_c_x-y3c_c_x2y376543K3XC_c_21一BX->.c_2|Bx22|一Bx32|_kBN-BN2BN3c_c_c_x3y2c_x-y2c_c_x2y3c_忑42I1BQ_x2X3y-J-2Ij2y及2|一mN3X3j21JTT忑42|一忑配2l一'JB把BJx3JX2忑8B忑弑FLc_x-y2c_C_x-y3c_x3y2c_c_x-y2c_x-y3c_x2y-C_>Rc_x-y3C_x3y-c_x-y2c_c_x-y3c_x3y-C_忑c_,01.2.系统准能计算薛定渭方程ih-tH利用演化算子Ut,0有tUt,00(

6、2)将(2)式代入(1)式得ihUtt,00HUt,00因此有ih-Utt,0HUt,0已知U0,0UiiU21U31U41ihtU51U61U71U81UUUUUUUU1是么次邱车，12U13U1422U23U2432U33U3442U43U4452U53U5462U63U6472U73U7482U83U84求TU15U25U35U45U55U65U75U852U16U26U36U46U56U66U76U86时的矩阵U17U18U27U28U37U38U47U48U57U58U67U68U77U78U87U88UT,0.HHHHHHHH1121314151617181HHHHHHHH1222

7、324252627282HHHHHHHH1323334353637383HUHHHHHH1424344454647484H15H25H35H45H55H65H75H85H16H26H36H46H56H66H76H86H17H27H37U47U57U67U77H87H18H28H38H48H58H68H78H88UUUUUUUU1121314151617181UUUUUUUU1222324252627282UUUUUUUU1323334353637383UUUUUUUU1424344454647484UUUUUUUU1525354555657585UUUUUUUU1626364656667686

8、UUUUUUUU1727374757677787UUUUUUUU1828384858687888ih-Uij8Hikk1Uj,i1,2,L.8.j1,2,L8.(5)如果定义H11H21H31H41NH51H61H71H81HHHHHHHH1222324252627282H13H23H33H43H53H63H73H83H14U24H34H44H54H64H74H84H15H25H35H45H55H65H75H85H16HH26HH36HH46UH56UH66UH76UH86H1727374757677787HHHHHHHH1828384858687888UUUUUUUU112131415161

9、7181UUUUUUUU1222324252627282UUUUUUUU1323334353637383UUUUUUUU1424344454647484UUUUUUUU1525354555657585UUUUUUUU1626364656667686UUUUUUUU1727374757677787UUUUUUUU182838485868788845则有:ih-UjtNj.初始条件：即：Uj 0,0 i 小,5 0,0 i .1U 0,010 0 00 10 00 0 100 0 0 10 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

10、10 0 00 10 00 0 100 0 0 1其中：8Nij HikU1 1,2,L8. j 1,2,L 8k 1(6)(8)(9)如果采取无量纲化，则(5)式变为-UtUij8 Hiki Ukj,i 1,2,L 8. j 1,2,L 8.k 1 h令tt,HHh，则有8Ut UijiHikUkj,i1,2,L8.j1,2,L8.k1然后求得解U(T,0)(其中T2/)的本征值，即将U(T,0)对角化，当U(T,0)的本征值虚部大于等于零，准能等于iarccosrealUiT,0,如果U(T,0)的本征值虚部小于零准能等于iarccosrealUiT,0.然后改变参数B；,其余参数表示成B

11、；的函数，对每一个B；的值有一个对应的i(i1,2,3,4,5,6,7,8),最后将相应的八个值用scatter画在同一张图上。系统准能计算主程序：znzcxclearjj=0；forn=1:1000Bz10=n.*0.01;XX0=eye(8);X0=reshape(XX0,1,64);t,X=ode45(ysjyhnew,0:0.01:2*pi,X0,Bz10);L=size(X);N=L(1,1);U1=reshape(X(N,:),8,8);U=U1.;UU=eig(U);forii=1:8e(n,ii)=-angle(UU(ii)/(2*pi);scatter(Bz10,e(n,ii

12、),5,k)holdonjj=jj+1;vx(jj)=Bz10;vy(jj)=e(n,ii);endy=vx;vy;fid=fopen(zn.dat,w);fprintf(fid,%12.8f%12.8fn,y);fclose(fid);endxlabel(fontsize14rmB_z10,Color,k)ylabel(fontsize24rmepsilon/omega,Color,k)gridonboxon系统准能计算函数程序:functionf=ysjyhnew(t,X,Bz10)w=1;Bz1=1.0.*Bz10.*cos(w.*t);Bz2=1.0.*Bz10.*cos(w.*t);

13、Bz3=1.0.*Bz10.*cos(w.*t);Bx1=1.0.*Bz10.*cos(w.*t);Bx2=1.0.*Bz10.*cos(w.*t);Bx3=1.0.*Bz10.*cos(w.*t);Jxy1221=0.2.*Bz10;Jxy2332=0.2.*Bz10;Jxy1331=0.2.*Bz10;H=zeros(8,8);H(1,1)=1/2*(Bz1+Bz2+Bz3);H(1,2)=-1/2*Bx3;H(1,3)=-1/2*Bx2;H(1,4)=Jxy2332;H(1,5)=-1/2*Bx1;H(1,6)=Jxy1331;H(1,7)=Jxy1221;H(1,8)=0;H(2,1)

14、=H(1,2);H(2,2)=1/2*(Bz1+Bz2-Bz3);H(2,3)=Jxy2332;H(2,4)=-1/2*Bx2;H(2,5)=Jxy1331;H(2,6)=-1/2*Bx1;H(2,7)=0;H(2,8)=Jxy1221;H(3,1)=H(1,3);H(3,2)=H(2,3);H(3,3)=1/2*(Bz1-Bz2+Bz3);H(3,4)=-1/2*Bx3;H(3,5)=Jxy1221;H(3,6)=0;H(3,7)=-1/2*Bx1;H(3,8)=Jxy1331;H(4,1)=H(1,4);H(4,2)=H(2,4);H(4,3)=H(3,4);H(4,4)=-1/2*(-B

15、z1+Bz2+Bz3);H(4,5)=0;H(4,6)=Jxy1221;H(4,7)=Jxy1331;H(4,8)=-1/2*Bx1;H(5,1)=H(1,5);H(5,2)=H(2,5);H(5,3)=H(3,5);H(5,4)=H(4,5);H(5,5)=-1/2*(Bz1-Bz2-Bz3);H(5,6)=-1/2*Bx3;H(5,7)=-1/2*Bx2;H(5,8)=Jxy2332;H(6,1)=H(1,6);H(6,2)=H(2,6);H(6,3)=H(3,6);H(6,4)=H(4,6);H(6,5)=H(5,6);H(6,6)=-1/2*(Bz1-Bz2+Bz3);H(6,7)=J

16、xy2332;H(6,8)=-1/2*Bx2;H(7,1)=H(1,7);H(7,2)=H(2,7);H(7,3)=H(3,7);H(7,4)=H(4,7);H(7,5)=H(5,7);H(7,6)=H(6,7);H(7,7)=-1/2*(Bz1+Bz2-Bz3);H(7,8)=-1/2*Bx3;H(8,1)=H(1,8);H(8,2)=H(2,8);H(8,3)=H(3,8);H(8,4)=H(4,8);H(8,5)=H(5,8);H(8,6)=H(6,8);H(8,7)=H(7,8);H(8,8)=-1/2*(Bz1+Bz2+Bz3);H;HU=-1i.*H*.X(1)X(2)X(3)X(

17、4)X(5)X(6)X(7)X(8);.X(9)X(10)X(11)X(12)X(13)X(14)X(15)X(16);.X(17)X(18)X(19)X(20)X(21)X(22)X(23)X(24);.X(25)X(26)X(27)X(28)X(29)X(30)X(31)X(32);.X(33)X(34)X(35)X(36)X(37)X(38)X(39)X(40);.X(41)X(42)X(43)X(44)X(45)X(46)X(47)X(48);.X(49)X(50)X(51)X(52)X(53)X(54)X(55)X(56);.X(57)X(58)X(59)X(60)X(61)X(62

18、)X(63)X(64);f=reshape(HU.',64,1);4.图1 .计算参数：w=1;Bz1=1.0.*Bz10.*cos(w.*t);Bz2=1.0.*Bz10.*cos(w.*t);Bz3=1.0.*Bz10.*cos(w.*t);Bx1=1.0.*Bz10.*cos(w.*t);Bx2=1.0.*Bz10.*cos(w.*t);Bx3=1.0.*Bz10.*cos(w.*t);Jxy1221=2.0.*Bz10;Jxy2332=2.0.*Bz10;Jxy1331=2.0.*Bz10;2 .计算参数：3.动力学方程含时薛定谓方程令：ihHt8C.1(2)其中：1000，2

19、.001,3其中：11000)，7>110；12)为纠缠态.将(1)改写为如下形式：010,4011,5100,6101,7110,8111.001，81113010,5100)；4)011),6)1101).iH将(2)式代入(3)式得：iHtttttCt整理得：C18C18C18C1iH8C18C18C：H.188C:H1 18C.H1其中1,2,L8ClHllH12H13H14H15H16H17H18C1C2H21H22H23H24H25H26H27H28C2C3H31H32H33H34H35H36H37H38C3C4H41H42H43H44H45H46H47H48C4C5iH51

20、H52H53H54H55H56H57H58C5C6H61H62H63H64H65H66H67H68C6C7H71H72H73H74H75H76H77H78C7C8H81H82H83H84H85H86H87H88C8动力学计算主程序:dlxzcxclearb=50;Bz10=0.118;x1=0.07x2=sqrt(1-2*x1A2)/sqrt(2)X0=x1*exp(i*pi*0.0)00x2*exp(i*pi*0.0)0x1*exp(i*pi*0.0)x2*exp(i*pi*0.0)0;%x3=1/sqrt(2)%x4=sqrt(1-1*x3A2)/sqrt(1)%X0=x3*exp(i*p

21、i*0.0)000*x2*exp(i*pi*0)0x4*exp(i*pi*0)0*x4*exp(i*pi*0)0;%X0=1*exp(i*pi*0.0)0000010./sqrt(2);X0=10000000;t,X=ode45(dlxfcnew,0:0.01:b,X0,Bz10);plot(t,(abs(X(:,1).A2,t,(abs(X(:,2).A2,t,(abs(X(:,3).A2,t,(abs(X(:,4).A2,t,(abs(X(:,5).A2,t,(abs(X(:,6).A2,t,(abs(X(:,7).A2,t,(abs(X(:,8).A2,'LineWidth

22、9;,2)xlabel('fontsize14rmt','Color','k')ylabel('fontsize14rm|C_alpha|A2','Color','k')legend('|1>','|2>','|3>','|4>','|5>','|6>','|7>','|8>')axis(0b01)gridonfigurepl

23、ot(t,(abs(X(:,1).A2+(abs(X(:,2).A2+(abs(X(:,3).A2+(abs(X(:,4).A2+(abs(X(:,5).A2+(abs(X(:,6).A2+(abs(X(:,7).A2+(abs(X(:,8).A2,'-k','LineWidth',2)xlabel('fontsize14rmt','Color','k')ylabel('fontsize14rmSigma_alpha|C_alpha|A2','Color','k')a

24、xis(0b01.2)gridonform=1:8figurey1=real(X(:,m);y2=imag(X(:,m);y=(abs(X(:,m).A2;%plot(t,y,'-k',t,y1,':k',t,y2,'-.k','LineWidth',2)plot(t,y,'-k',t,y1,'-r',t,y2,'-b','LineWidth',2)%plot(t,y,'-k','LineWidth',2)xlabel('fon

25、tsize14rmt','Color','k')yy1='fontsize14rmreal(C_',int2str(m),')'yy2='fontsize14rmimag(C_',int2str(m),')'yy='fontsize14rm|C_',int2str(m),'F2'ylabel(yy,'Color','k')legend(yy,yy1,yy2)axis(0b-1.01.0)gridonendforii=1:size

26、(t)vt(ii)=t(ii);forn=1:8x(ii,n)=(abs(X(ii,n).A2;vx(ii,n)=real(X(ii,n);vy(ii,n)=imag(X(ii,n);endendy=vt',x,vx,vy;yy=y'fid=fopen('dlx.dat','w');fprintf(fid,'%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12.8f%12

27、.8f%12.8f%12.8f%12.8f%12.8f%12.8fn',yy);fclose(fid);动力学计算函数程序:functionf=dlxfcnew(t,X,Bz10)w=1;Bz1=1.0.*Bz10.*cos(w.*t);Bz2=1.0.*Bz10.*cos(w.*t);Bz3=1.0.*Bz10.*cos(w.*t);Bx1=1.0.*Bz10.*cos(w.*t);Bx2=1.0.*Bz10.*cos(w.*t);Bx3=1.0.*Bz10.*cos(w.*t);Jxy1221=2.0.*Bz10;Jxy2332=2.0.*Bz10;Jxy1331=2.0.*Bz1

28、0;H=zeros(8,8);H(1,1)=1/2*(Bz1+Bz2+Bz3);H(1,2)=-1/2*Bx3;H(1,3)=-1/2*Bx2;H(1,4)=Jxy2332;H(1,5)=-1/2*Bx1;H(1,6)=Jxy1331;H(1,7)=Jxy1221;H(1,8)=0;H(2,1)=H(1,2);H(2,2)=1/2*(Bz1+Bz2-Bz3);H(2,3)=Jxy2332;H(2,4)=-1/2*Bx2;H(2,5)=Jxy1331;H(2,6)=-1/2*Bx1;H(2,7)=0;H(2,8)=Jxy1221;H(3,1)=H(1,3);H(3,2)=H(2,3);H(3,3

29、)=1/2*(Bz1-Bz2+Bz3);H(3,4)=-1/2*Bx3;H(3,5)=Jxy1221;H(3,6)=0;H(3,7)=-1/2*Bx1;H(3,8)=Jxy1331;H(4,1)=H(1,4);H(4,2)=H(2,4);H(4,3)=H(3,4);H(4,4)=-1/2*(-Bz1+Bz2+Bz3);H(4,5)=0;H(4,6)=Jxy1221;H(4,7)=Jxy1331;H(4,8)=-1/2*Bx1;H(5,1)=H(1,5);H(5,2)=H(2,5);H(5,3)=H(3,5);H(5,4)=H(4,5);H(5,5)=-1/2*(Bz1-Bz2-Bz3);H(5

30、,6)=-1/2*Bx3;H(5,7)=-1/2*Bx2;H(5,8)=Jxy2332;H(6,1)=H(1,6);H(6,2)=H(2,6);H(6,3)=H(3,6);H(6,4)=H(4,6);H(6,5)=H(5,6);H(6,6)=-1/2*(Bz1-Bz2+Bz3);H(6,7)=Jxy2332;H(6,8)=-1/2*Bx2;H(7,1)=H(1,7);H(7,2)=H(2,7);H(7,3)=H(3,7);H(7,4)=H(4,7);H(7,5)=H(5,7);H(7,6)=H(6,7);H(7,7)=-1/2*(Bz1+Bz2-Bz3);H(7,8)=-1/2*Bx3;H(8

31、,1)=H(1,8);H(8,2)=H(2,8);H(8,3)=H(3,8);H(8,4)=H(4,8);H(8,5)=H(5,8);H(8,6)=H(6,8);H(8,7)=H(7,8);H(8,8)=-1/2*(Bz1+Bz2+Bz3);H;HU=-1i.*H*X(1);X(2);X(3);X(4);X(5);X(6);X(7);X(8);f=reshape(HU.',8,1);1.参数:w=1;Bz1=1.0.*Bz10.*cos(w.*t);Bz2=1.0.*Bz10.*cos(w.*t);Bz3=1.0.*Bz10.*cos(w.*t);Bx1=1.0.*Bz10.*cos(

32、w.*t);Bx2=1.0.*Bz10.*cos(w.*t);Bx3=1.0.*Bz10.*cos(w.*t);Jxy1221=2.0.*Bz10;Jxy2332=2.0.*Bz10;Jxy1331=2.0.*Bz10;Bz10=0.118;X0=10000000;口 40?I .U .10 5DICL0/脸-0?0n?Gw °-03，口 Gio X一晔萌CJ皿沁）i.力4.密度矩阵定义1:1000,2001,3010,4011,5100,6.101,7110,8111(2)定义2:100,201,310,|411.按定义2将定义1表示为如下形式1000)110)田0,2)001)1

33、111,3010)120)0)，4)011)1211,5；100)13。)0),6)101)1311,7)110)140140),8)111141)1.则有：C11G2C33C44.C55.C66,C77C88C1000：C2001.C3010C4011C5100.C6101C7110C8111C1I10C2I11C3I20IC4I21C5I30C6131C7I40,C8141.C110.C211C320C421C530C631C740c841定义密度矩阵：IXI对0,1求迹1T01C110.C211C3I20.C4210C53*C11*.C5310.00C63*C21*.C63|C7|4*C

34、32*.C74C8|4*C42*.C840C21*.C11*.C21C11C21Cl1C32C53C7I4c4*C32*.C42C32c4|2C6|3*一.C53l*.C63C53C6|3C8|4-*.C74*.C84C74C8|4101*.C11*.C21|*.C32*.C42*一.*.C53|C74_*._*.C63C84C11C3I2C5I3C7I4C11C2I1C42C6|3C84C21*.C1C1111*C3C1*C5C1C7C1*C2c2*C4C2C6c2*2 13 14 11 12 13 1C8c2I41*C1C1C3C1*C5c1C7c1C12C3C1C5c1C7C1*.-.C

35、1C3|12C3C3I22*.c5c313*2*.C7c3I4；（2_*.c2c4田；2*c4c4I2/.2C6c41*2c8c4I42C1C5I13c3c5123c5c5133l*.c7c5143* .c2c6|13* .C4C6123c6c6133C8c6I43*.*.*.C32C53C74*.*.C42C63C84*.-.C1C7I14C3C7I24|C5C7I34*.C7C7I44c2c8|14*C4c8I2）（4c6c813八4_*c8c8144|*C2c2C4C2*C6c2C8c2111121131|41*C1C3C3C*C5C3c7c3C2C4|12C4c4|22C6C4I32C

36、8c4|42*C1C5C3C5*C5c5C7c5c2c6|13C4C；123C6C；133lC8C；|43C22111c4c2121c6c2131c8c2141C1C3C2C4|12C32C42|22lc5c3c6c4I32c7c3c8c4142C1C5C2C；|13C3C5c4c6123C52C62133*C7c5C8C*143C1C7C2c8|14lC3c7C4C8|24c5c7c6c8I34c7c7c8c8144C1C7C2C*114c3c7c4c8124c5c7c6c8I34C72C82|44因此有：C12*C3C1*C5C1*C7C1C22*C4C2*C6C2*C8C2*C1C3C3

37、2*C5c3*C7c3*c2c4C42*C6C4*C8C4*C1C5*C3c5C52*C7c5*C2C6*C4C6C62*C8C6*C1C7*C3c7*C5c7C72*C2C8*C4C8*C6C8C82*yC12C1C3C1C5*C1C7yC22c2cC2C*4*6*C1C7*C1C5*C1C3C122C7*C7C5*C7C3*C7C1*C2C8C12*C1C3*C1C5*C1C7_*C3C1C32C3C5*C3C72C2*C2c4*C2c6*C2c8C4C2C42C4CC4C*C2c6C2CC82*C8c6*C8c4*C8c21.计算厄密矩阵本征值其中i是的本征值，而2.计算C令：ee*6*

38、8*C3C5*C3C7C5C1C5C3C52*C5C7C4c2C42*C4c6*C4c8C6C2C6C4C62*C6C8_*C5C1*C5c3C52*C5C7C7C1C7C3*C7C5C72C6c2*C6c4C62*C6c8C8C2C8c4C8C6C82C7C1*C7c3*C7C5C72C8c2*C8c4*C8c6C82yC12*C1C3*C1C5*C1C7C22*C2C4*C2C6*C2C8*C3C1C32*C3C5*C3C7*C4C2C42*C4C6*C4C8*C5G*C5C3C52*C5C7*C6c2*C6C4C62*C6C8*C7C1*C7c3*C7c5*C8c2C8cC8c*4*6*

39、C3C7*C3C5C32*C3C1*C5C72C5*C5C3*C5C1*C4c8*C4C6C42*C4C2*C5C7C52*C5C3*C5C1*C6c8C62*C6C4*C6c2C72*C7c5*C7c3*C7C1*C8c6*C8C4*C8c20001001001001000*C6c8C62*C6c4*C6C2*C3C7*C3C5C32*C3C1*C4c8*C4C6C42*C4C2*C1C7*C1C5*C1C3C12*C2c8*C2c6*C2C42C2%i1,2,3,4为对应的本征函数/,按照降序排列i,然后计算Ceemax34,03.绘制Cee与时间t的函数关系.计算主程序：Ceezcxcl

40、earb=100;T=0:0.01:b;Bz10=0.118;X0=10000000;t,X=ode45(dlxfcnew,T,X0,Bz10);N=max(size(T);form=1:8forn=1:NC(n,m)=X(n,m);endendforn=1:NR=C(n,1)*conj(C(n,1)+C(n,2)*conj(C(n,2),C(n,1)*conj(C(n,3)+C(n,2)*conj(C(n,4),C(n,1)*conj(C(n,5)+C(n,2)*conj(C(n,6),C(n,1)*conj(C(n,7)+C(n,2)*conj(C(n,8);.C(n,3)*conj(C(

41、n,1)+C(n,4)*conj(C(n,2),C(n,3)*conj(C(n,3)+C(n,4)*conj(C(n,4),C(n,3)*conj(C(n,5)+C(n,4)*conj(C(n,6),C(n,3)*conj(C(n,7)+C(n,4)*conj(C(n,8);.C(n,5)*conj(C(n,1)+C(n,6)*conj(C(n,2),C(n,5)*conj(C(n,3)+C(n,6)*conj(C(n,4),C(n,5)*conj(C(n,5)+C(n,6)*conj(C(n,6),C(n,5)*conj(C(n,7)+C(n,6)*conj(C(n,8);.C(n,7)*c

42、onj(C(n,1)+C(n,8)*conj(C(n,2),C(n,7)*conj(C(n,3)+C(n,8)*conj(C(n,4),C(n,7)*conj(C(n,5)+C(n,8)*conj(C(n,6),C(n,7)*conj(C(n,7)+C(n,8)*conj(C(n,8);RR=0,0,0,-1;0,0,1,0;0,1,0,0;-1,0,0,0*conj(R)*0,0,0,-1;0,0,1,0;0,1,0,0;-1,0,0,0;A=R*RR;bc=eig(A);AA=sqrt(c(1,1),sqrt(c(2,2),sqrt(c(3,3),sqrt(c(4,4);%A=sqrtm(sqrtm(R)*RR*sqrtm(R);bc=eig(A);AA=c(1,1),c(2,2),c(3,3),c(4,4);B=sort(AA,'descend');Cee(n)=max(B(1)-B(2)-B(3)-B(4),0);endplot(t,(r