My matlab code:
function chi = Solve_chi(eps,y,n,AllPau,Phi)
d = 2^n;cvx_begin
variable chi(d^2,d^2) hermitian;
chi == hermitian_semidefinite(d^2);minimize(norm(vec(chi),1));
subject to
norm(y-Phi*vec(chi),2) <= eps;
chi >= 0;
E2 = zeros(d);
for i=1:16
for j=1:16
E2 = E2+chi(i,j)*AllPau{j}'*AllPau{i};
end
end
E2 == eye(d);cvx_end
end
What I get for chi is a 16*16 matrix with all element NaN + NaNi. It is wrong clearly. While I know using for-loop may cause problem, but I don’t know other method to express \sum_{\alpha, \beta} \chi_{\alpha \beta} \Gamma_\beta^{\dagger} \Gamma_\alpha=I_d.