Code for optimal measurements

clear all; clc;
[x,y,z]=sphere;
surf(x,y,z,'FaceAlpha',.3,'EdgeColor','none');
hold on;
phi = pi/5;
ori = [sqrt(3)/2;0.5*exp(1j*phi)];
vec = State2Vector(ori);
quiver3(0,0,0,vec(1),vec(2),vec(3),'yellow');
L = 2*[0 -sqrt(3)/4*1j*exp(-1j*phi); sqrt(3)/4*1j*exp(1j*phi) 0];
M = [1/4 -sqrt(3)/4*exp(-1j*phi); -sqrt(3)/4*exp(1j*phi) 3/4];
quiver3(0,0,0,1,0,0);quiver3(0,0,0,0,1,0);quiver3(0,0,0,0,0,1);
for a = -100:0.1:100
    Tmp = L;
    Tmp = Tmp + a*M;
    [V,D]=eig(Tmp);
    state = V(:,1);
    vec = State2Vector(state);
    scatter3(vec(1),vec(2),vec(3),'filled'); hold  on;
end

where yellow arrow stands for parametrized state.