How to use an external calculator

We will see how to use an external calculator. For example, suppose you have a reduced density operator $\tilde\rho_{1,2}$ in the read-line mode:

 > init-mixed 0.7 0.7 0.9;
 > H(1 2);CN(1 2,3);
 > RDO(1 2);
0.25|0><0| + 0.1|0><1| + 0.1|0><2| + 0.1|1><0| + 0.25|1><1| + 
0.04|1><2| + 0.1|2><0| + 0.04|2><1| + 0.25|2><2| + 0.25|3><3|
 > SvNRDO(1 2)
1.87811

As we have seen above, the von Neumann entropy of $\tilde\rho_{1,2}$ is $S_{vN}(\tilde\rho_{1,2})=1.87811$.

This matrix can be saved and converted to the matrix in the style of Octave by the commands:

 > RDOsave(1 2, foo.matrix);
 > conv-octave(foo.matrix, foo.matrix.octave);

The file ``foo.matrix.octave'' contains the text:

[2.500000000e-01,1.000000000e-01,1.000000000e-01,0;1.000000000e-01,2.500000000e-
01,4.000000000e-02,0;1.000000000e-01,4.000000000e-02,2.500000000e-01,0;0,0,0,2.5
00000000e-01]

Then you can calculate the von Neumann entropy $S_{vN}(\tilde\rho_{1,2})$ also by using Octave. The Octave function to calculate $S_{vN}(\rho)$ for a density matrix $\rho$ is

%%%% The Octave function to calculate the von Neumann entropy of rho %%%%
function S = SvN(rho)
   A = eig(rho);
   S = 0;
   for i=1:1:rows(A)
      if A(i,1) ~= 0,
         S += A(i,1)*log(A(i,1))/log(2);
      endif
   endfor
   S = -S;
endfunction

This function and the rest part of the program

A=[2.500000000e-01,1.000000000e-01,1.000000000e-01,0;1.000000000e-01,2.500000000e
-01,4.000000000e-02,0;1.000000000e-01,4.000000000e-02,2.500000000e-01,0;0,0,0,2.5
00000000e-01];
SvN(A)

returns the result $S_{vN}(\tilde\rho_{1,2})=1.8781$ as shown below.

[akira@localhost transition]$ octave foo.octave
GNU Octave, version 2.1.35 (i386-redhat-linux-gnu).
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001 John W. Eaton.
This is free software with ABSOLUTELY NO WARRANTY.
For details, type `warranty'.

ans = 1.8781

This value is equal to the one obtained by silqcs.