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We consider a protocol to perform the optimal quantum state discrimination of  $N$ linearly independent non-orthogonal pure quantum states and present acomputational code. Through the extension of the original Hilbert space, it ispossible to perform an unitary operation yielding a final configuration, whichgives the best discrimination without ambiguity by means of von Neumannmeasurements. Our goal is to introduce a detailed general mathematicalprocedure to realize this task by means of semidefinite programming and normminimization.  The former is used to fix which is the best detection probability amplitudefor each state of the ensemble. The latter determines the matrix which leadsthe states to the final configuration. In a final step, we decompose theunitary transformation in a sequence of two-level rotation matrices.Comment: 12 pages, including a matlab cod

AN ALGORITHM TO PERFORM POVMS THROUGH NEUMARK THEOREM: APPLICATION TO THE DISCRIMINATION OF NON-ORTHOGONAL PURE QUANTUM STATES