> psi:=evalm( (1/13) * matrix(2,1,[5,-12*I]) ):
RKet(psi);

5/13*`|0>`-12/13*I*`|1>`

> # psi:=matrix(2,1,[aa,bb]):
# RKet(psi);

>
RKet(Bell||0||0);

1/2*sqrt(2)*`|00>`+1/2*sqrt(2)*`|11>`

> phi:=kr(psi,Bell||0||0):
RKet(phi);

5/26*sqrt(2)*`|000>`+5/26*sqrt(2)*`|011>`-6/13*I*sq...

> for i from 0 to 1 do for j from 0 to 1 do
Proj||i||j:=kr(Ket_To_Rho(Bell||i||j),diag(1,1)):
# print(i,j, evalm(Proj||i||j)):
od; od:

> for i from 0 to 1 do for j from 0 to 1 do
phi||i||j:=evalm(Proj||i||j &* phi);
print(i,j,RKet(phi||i||j));
print(`Bell`,i,j,``=``,RKet(Bell||i||j)) ;
od; od;

0, 0, 5/52*sqrt(2)*`|000>`-3/13*I*sqrt(2)*`|001>`+5...

Bell, 0, 0, `` = ``, 1/2*sqrt(2)*`|00>`+1/2*sqrt(2)...

0, 1, -3/13*I*sqrt(2)*`|010>`+5/52*sqrt(2)*`|011>`-...

Bell, 0, 1, `` = ``, 1/2*sqrt(2)*`|01>`+1/2*sqrt(2)...

1, 0, 3/13*I*sqrt(2)*`|010>`+5/52*sqrt(2)*`|011>`-3...

Bell, 1, 0, `` = ``, 1/2*sqrt(2)*`|01>`-1/2*sqrt(2)...

1, 1, 5/52*sqrt(2)*`|000>`+3/13*I*sqrt(2)*`|001>`-5...

Bell, 1, 1, `` = ``, 1/2*sqrt(2)*`|00>`-1/2*sqrt(2)...

> for i from 0 to 1 do for j from 0 to 1 do
nn||i||j:=norm(phi||i||j,2);
Prob||i||j:=nn||i||j^2;
Phi||i||j:=evalm((1/nn||i||j) * phi||i||j);
print(i,j,Prob||i||j, RKet(Phi||i||j));
od;od;

0, 0, 1/4, 5/26*sqrt(2)*`|000>`-6/13*I*sqrt(2)*`|00...

0, 1, 1/4, -6/13*I*sqrt(2)*`|010>`+5/26*sqrt(2)*`|0...

1, 0, 1/4, 6/13*I*sqrt(2)*`|010>`+5/26*sqrt(2)*`|01...

1, 1, 1/4, 5/26*sqrt(2)*`|000>`+6/13*I*sqrt(2)*`|00...

> U||0||0:=kr(diag(1,1,1,1), SSS||0):
U||0||1:=kr(diag(1,1,1,1), SSS||1):
U||1||0:=kr(diag(1,1,1,1), evalm(I * SSS||2) ):
U||1||1:=kr(diag(1,1,1,1), SSS||3):

> for i from 0 to 1 do for j from 0 to 1 do
print(i,j,sort(RKet(evalm( U||i||j &* Phi||i||j))));
print(`Bell`,i,j,``=``,RKet( kr(Bell||i||j,psi) ) );
print(`***`);
od; od;

0, 0, -6/13*I*sqrt(2)*`|111>`-6/13*I*sqrt(2)*`|001>...

Bell, 0, 0, `` = ``, -6/13*I*sqrt(2)*`|111>`-6/13*I...

`***`

0, 1, 5/26*sqrt(2)*`|010>`+5/26*sqrt(2)*`|100>`-6/1...

Bell, 0, 1, `` = ``, 5/26*sqrt(2)*`|010>`+5/26*sqrt...

`***`

1, 0, 5/26*sqrt(2)*`|010>`-5/26*sqrt(2)*`|100>`-6/1...

Bell, 1, 0, `` = ``, 5/26*sqrt(2)*`|010>`-5/26*sqrt...

`***`

1, 1, 6/13*I*sqrt(2)*`|111>`-6/13*I*sqrt(2)*`|001>`...

Bell, 1, 1, `` = ``, 6/13*I*sqrt(2)*`|111>`-6/13*I*...

`***`

>