  The optimization conditions for minimum error discrimination of linearly
independent pure states comprise of two kinds: stationary conditions over the
space of rank one projective measurements and the global maximization
conditions. A discrete number of projective measurments will solve th former of
which a unique one will solve the latter. In the case of three real linearly
independent pure states we show that the stationary conditions translate to a
system of simultaneous polynomial (non linear) equations in three variabes thus
explaining why it's so difficult to obtain a closed-form solution for the
optimal POVM. Additionally, our method suggests that as an ensemble of LI pure
states is varied as a smooth function of some independent parameters, the
optimal POVM will also vary smoothly as a function of the same parameters. By
employing the implicit functions theorem we exploit this fact to obtain a
technique to find the solution of MED of LI pure states by dragging the
solution from a known example (say, pure orthogonal states) to any general
linearly indepenent ensemble of pure states in the same Hilbert space. By
employing RK4 to solve the first order coupled non-linear differential
equations find that the resulting error is within the RK4 error performance.
