partial_transpose

function [Partial_Transpose,Negativity] = ptranspose(A,m,n);
% This function takes a bipartite density matrix A and submatrix dimensions 
% m,n. It then calculates partial transpose, its eigenvalues and if the 
% partial transpose is square, negativity. Matlab can only find eigenvalues
% of a square matrix. This is accomplished by separating the density matrix's
% indices into submatrices of size m,n and taking their transpose. If any of
% the eigenvalues are negative, A is not a physically acceptable state. If 
% Negativity is not 0, the state is inseperable. If the  If the negativity is
% positive the state is inseperable.

s = size(A);
x = s(1,1)/n;
y = s(1,2)/n;

b= zeros(n*m);
c = zeros(n,n);
        
        for i = 1:x;      
        
            for j = 1:y;
                
                t = A(((n*(i-1)+1):n*i),(((n*(j-1)+1)):n*j));
                T = t';
                b(((n*(i-1)+1):n*i),(((n*(j-1)+1)):n*j)) = T;
                
                if i ~= j
                
               c((((n*(j-1)+1)):n*j),((n*(i-1)+1):n*i)) = t;
               
                end
                
                 if i == j
                 
               c((((n*(j-1)+1)):n*j),((n*(i-1)+1):n*i)) = c((((n*(j-1)+1)):n*j),((n*(i-1)+1):n*i)) + t;
               
           end
                  
          end
        
        end
         
        ptr_1 = c
        
        ptr_2 = b
        
    
end