  Inspired by the work done by Belavkin [Belavkin V. P., Stochastics, 1, 315
(1975)], and independently by Mochon, [Phys. Rev. A 73, 032328, (2006)], we
formulate the problem of minimum error discrimination of any ensemble of $n$
linearly independent pure states by stripping the problem of its rotational
covariance and retaining only the rotationally invariant aspect of the problem.
This is done by embedding the optimal conditions in a matrix equality as well
as matrix inequality. Employing the implicit function theorem in these
conditions we get a set of first-order coupled ordinary non-linear differential
equations which can be used to drag the solution from an initial point (where
solution is known) to another point (whose solution is sought). This way of
obtaining the solution can be done through a simple Taylor series expansion and
analytic continuation when required. Thus, we \emph{complete} the work done by
Belavkin and Mochon by ultimately leading their theory to a solution for the
minimum error discrimination problem of linearly independent pure state
ensembles. We also compare the computational complexity of our technique with a
barrier-type interior point method of SDP and show that our technique is
computationally as efficient as (actually, a bit more than) the SDP algorithm,
with the added advantage of being much simpler to implement.
