Alladi Ramakrishnan Hall

Minimum Error Discrimination For Linearly Independent States

Tanmay Singal

IMSc

Inspired by the work done by Belavkin [\url{Belavkin V. P. Stochastics, 1,
315 (1975)}] and C. Mochon [\url{Phys. Rev. A 73, 032328, (2006)}], we
formulate the problem of minimum error discrimination of an ensemble of n
linearly independent pure states by embedding the optimal conditions in a
matrix equation and matrix inequality. Employing the implicit function
theorem in this matrix equation 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 can be done through a simple Taylor
series expansion and analytic continuation when required. Thus we give a
technique to solve the MED problem for LI pure state ensembles based on
the theory of the aforementioned papers. Thus, along with our technique,
the work done by Belavkin and C. Mochon by gives an analytical solution
for the MED problem of LI pure state ensembles.