Room 117

Complete analysis for three-qubit mixed-state discrimination

Tanmay Singal

IMSc

In this article, by treating minimum error state discrimination as a
complementarity problem, we obtain the geometric optimality conditions.
These can be used as the necessary and sufficient conditions to determine
whether every optimal measurement operator can be nonzero. Using these
conditions and an inductive approach, we demonstrate a geometric method
and the intrinsic polytope for N-qubit mixed-state discrimination. When
the intrinsic polytope becomes a point, a line segment, or a triangle, the
guessing probability, the necessary and sufficient condition for the exact
solution, and the optimal measurement are analytically obtained. We apply
this result to the problem of discrimination to arbitrary three-qubit
mixed states with given a priori probabilities and obtain the complete
analytic solution to the guessing probability and optimal measurement.

Journal reference: journals.aps.org/pra/abstract/10.1103/PhysRevA.87.062302