Optimal Unambiguous Discrimination of Quantum States

Unambiguously distinguishing between nonorthogonal but linearly independent quantum states is a challenging problem in quantum information processing. In this work, an exact analytic solution to an optimum measurement problem involving an arbitrary number of pure linearly independent quantum states is presented. To this end, the relevant semi-definite programming task is reduced to a linear programming one with a feasible region of polygon type which can be solved via simplex method. The strength of the method is illustrated through some explicit examples. Also using the close connection between the Lewenstein-Sanpera decomposition(LSD) and semi-definite programming approach, the optimal positive operator valued measure for some of the well-known examples is obtain via Lewenstein-Sanpera decomposition method. {\bf Keywords:} Optimal Unambiguous State Discrimination, Linear Programming, Lewenstein-Sanpera decomposition. {\bf PACs Index: 03.67.Hk, 03.65.Ta, 42.50.-p