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.